3GPP TS 38.211 V19.0.0 (2025-06)

Technical Specification

3rd Generation Partnership Project;

Technical Specification Group Radio Access Network;

NR;

Physical channels and modulation

(Release 19)

    

Image    Image

 

The present document has been developed within the 3rd Generation Partnership Project (3GPP TM) and may be further elaborated for the purposes of 3GPP..The present document has not been subject to any approval process by the 3GPP<br> Organizational Partners and shall not be implemented.This Specification is provided for future development work within 3GPP<br> only. The Organizational Partners accept no liability for any use of this Specification.Specifications and <br>Reports for implementation of the 3GPP TM system should be obtained via the 3GPP Organizational Partners' Publications Offices.

 

 

 

 

Keywords

New Radio, Layer 1

 

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© 2025, 3GPP Organizational Partners (ARIB, ATIS, CCSA, ETSI, TSDSI, TTA, TTC).

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<br>Contents #

Foreword    8

1    Scope    9

2    References    9

3    Definitions of terms, symbols and abbreviations    9

3.1    Terms    9

3.2    Symbols    9

3.3    Abbreviations    11

4    Frame structure and physical resources    11

4.1    General    11

4.2    Numerologies    12

4.3    Frame structure    12

4.3.1    Frames and subframes    12

4.3.2    Slots    13

4.4    Physical resources    14

4.4.1    Antenna ports    14

4.4.2    Resource grid    14

4.4.3    Resource elements    14

4.4.4    Resource blocks    14

4.4.4.1    General    14

4.4.4.2    Point A    15

4.4.4.3    Common resource blocks    15

4.4.4.4    Physical resource blocks    15

4.4.4.5    Virtual resource blocks    15

4.4.4.6    Interlaced resource blocks    15

4.4.5    Bandwidth part    16

4.4.6    Common MBS frequency resource    16

4.5    Carrier aggregation    16

5    Generic functions    17

5.1    Modulation mapper    17

5.1.1    π/2-BPSK    17

5.1.2    BPSK    17

5.1.3    QPSK    17

5.1.4    16QAM    17

5.1.5    64QAM    17

5.1.6    256QAM    17

5.1.7    1024QAM    18

5.2    Sequence generation    18

5.2.1    Pseudo-random sequence generation    18

5.2.2    Low-PAPR sequence generation type 1    18

5.2.2.1    Base sequences of length 36 or larger    18

5.2.2.2    Base sequences of length less than 36    19

5.2.3    Low-PAPR sequence generation type 2    22

5.2.3.1    Sequences of length 30 or larger    22

5.2.3.2    Sequences of length less than 30    22

5.3    OFDM baseband signal generation    26

5.3.1    OFDM baseband signal generation for all channels except PRACH and RIM-RS    26

5.3.2    OFDM baseband signal generation for PRACH    28

5.3.3    OFDM baseband signal generation for RIM-RS    30

5.4    Modulation and upconversion    31

6    Uplink    31

6.1    Overview    31

6.1.1    Overview of physical channels    31

6.1.2    Overview of physical signals    31

6.2    Physical resources    31

6.2.1    Muting resource    32

6.3    Physical channels    32

6.3.1    Physical uplink shared channel    32

6.3.1.1    Scrambling    32

6.3.1.2    Modulation    33

6.3.1.2a    Inter-slot cover code    34

6.3.1.3    Layer mapping    34

6.3.1.4    Transform precoding    34

6.3.1.5    Precoding    35

6.3.1.6    Mapping to virtual resource blocks    60

6.3.1.7    Mapping from virtual to physical resource blocks    60

6.3.2    Physical uplink control channel    61

6.3.2.1    General    61

6.3.2.2    Sequence and cyclic shift hopping    61

6.3.2.2.1    Group and sequence hopping    61

6.3.2.2.2    Cyclic shift hopping    62

6.3.2.3    PUCCH format 0    62

6.3.2.3.1    Sequence generation    62

6.3.2.3.2    Mapping to physical resources    63

6.3.2.4    PUCCH format 1    63

6.3.2.4.1    Sequence modulation    63

6.3.2.4.2    Mapping to physical resources    64

6.3.2.5    PUCCH format 2    64

6.3.2.5.1    Scrambling    64

6.3.2.5.2    Modulation    65

6.3.2.5.2A    Spreading    65

6.3.2.5.3    Mapping to physical resources    65

6.3.2.6    PUCCH formats 3 and 4    66

6.3.2.6.1    Scrambling    66

6.3.2.6.2    Modulation    66

6.3.2.6.3    Block-wise spreading    66

6.3.2.6.4    Transform precoding    67

6.3.2.6.5    Mapping to physical resources    67

6.3.3    Physical random-access channel    68

6.3.3.1    Sequence generation    68

6.3.3.2    Mapping to physical resources    75

6.4    Physical signals    95

6.4.1    Reference signals    95

6.4.1.1    Demodulation reference signal for PUSCH    95

6.4.1.1.1    Sequence generation    95

6.4.1.1.2    (void)    97

6.4.1.1.3    Precoding and mapping to physical resources    97

6.4.1.2    Phase-tracking reference signals for PUSCH    102

6.4.1.2.1    Sequence generation    102

6.4.1.2.1.1    Sequence generation if transform precoding is not enabled    102

6.4.1.2.1.2    Sequence generation if transform precoding is enabled    102

6.4.1.2.2    Mapping to physical resources    103

6.4.1.2.2.1    Precoding and mapping to physical resources if transform precoding is not enabled    103

6.4.1.2.2.2    Mapping to physical resources if transform precoding is enabled    105

6.4.1.3    Demodulation reference signal for PUCCH    106

6.4.1.3.1    Demodulation reference signal for PUCCH format 1    106

6.4.1.3.1.1    Sequence generation    106

6.4.1.3.1.2    Mapping to physical resources    107

6.4.1.3.2    Demodulation reference signal for PUCCH format 2    107

6.4.1.3.2.1    Sequence generation    107

6.4.1.3.2.2    Mapping to physical resources    108

6.4.1.3.3    Demodulation reference signal for PUCCH formats 3 and 4    108

6.4.1.3.3.1    Sequence generation    108

6.4.1.3.3.2    Mapping to physical resources    108

6.4.1.4    Sounding reference signal    109

6.4.1.4.1    SRS resource    109

6.4.1.4.2    Sequence generation    109

6.4.1.4.3    Mapping to physical resources    111

6.4.1.4.4    Sounding reference signal slot configuration    117

7    Downlink    117

7.1    Overview    117

7.1.1    Overview of physical channels    117

7.1.2    Overview of physical signals    118

7.2    Physical resources    118

7.3    Physical channels    118

7.3.1    Physical downlink shared channel    118

7.3.1.1    Scrambling    118

7.3.1.2    Modulation    119

7.3.1.3    Layer mapping    120

7.3.1.4    Antenna port mapping    121

7.3.1.5    Mapping to virtual resource blocks    121

7.3.1.6    Mapping from virtual to physical resource blocks    121

7.3.2    Physical downlink control channel (PDCCH)    123

7.3.2.1    Control-channel element (CCE)    123

7.3.2.2    Control-resource set (CORESET)    123

7.3.2.3    Scrambling    125

7.3.2.4    PDCCH modulation    125

7.3.2.5    Mapping to physical resources    125

7.3.3    Physical broadcast channel    126

7.3.3.1    Scrambling    126

7.3.3.2    Modulation    126

7.3.3.3    Mapping to physical resources    126

7.4    Physical signals    126

7.4.1    Reference signals    126

7.4.1.1    Demodulation reference signals for PDSCH    126

7.4.1.1.1    Sequence generation    126

7.4.1.1.2    Mapping to physical resources    127

7.4.1.2    Phase-tracking reference signals for PDSCH    131

7.4.1.2.1    Sequence generation    131

7.4.1.2.2    Mapping to physical resources    131

7.4.1.3    Demodulation reference signals for PDCCH    133

7.4.1.3.1    Sequence generation    133

7.4.1.3.2    Mapping to physical resources    133

7.4.1.4    Demodulation reference signals for PBCH    134

7.4.1.4.1    Sequence generation    134

7.4.1.4.2    Mapping to physical resources    134

7.4.1.5    CSI reference signals    134

7.4.1.5.1    General    134

7.4.1.5.2    Sequence generation    135

7.4.1.5.3    Mapping to physical resources    135

7.4.1.6    RIM reference signals    138

7.4.1.6.1    General    138

7.4.1.6.2    Sequence generation    139

7.4.1.6.3    Mapping to physical resources    139

7.4.1.6.4    RIM-RS configuration    140

7.4.1.6.4.1    General    140

7.4.1.6.4.2    Time-domain parameters and mapping from \(i\text{t}\) to time-domain parameters    140

7.4.1.6.4.3    Frequency-domain parameters and mapping from \(i\text{f}\) to frequency-domain parameters    141

7.4.1.6.4.4    Sequence parameters and mapping from \(i\text{s}\) to sequence parameters    141

7.4.1.6.4.5    Mapping between resource triplet and set ID    141

7.4.1.7    Positioning reference signals    142

7.4.1.7.1    General    142

7.4.1.7.2    Sequence generation    142

7.4.1.7.3    Mapping to physical resources in a downlink PRS resource    142

7.4.1.7.4    Mapping to slots in a downlink PRS resource set    143

7.4.2    Synchronization signals    144

7.4.2.1    Physical-layer cell identities    144

7.4.2.2    Primary synchronization signal    144

7.4.2.2.1    Sequence generation    144

7.4.2.2.2    Mapping to physical resources    144

7.4.2.3    Secondary synchronization signal    145

7.4.2.3.1    Sequence generation    145

7.4.2.3.2    Mapping to physical resources    145

7.4.3    SS/PBCH block    145

7.4.3.1    Time-frequency structure of an SS/PBCH block    145

7.4.3.1.1    Mapping of PSS within an SS/PBCH block    146

7.4.3.1.2    Mapping of SSS within an SS/PBCH block    147

7.4.3.1.3    Mapping of PBCH and DM-RS within an SS/PBCH block    147

7.4.3.2    Time location of an SS/PBCH block    147

7.4.4    Wake-up signal    147

7.4.4.1    Sequence generation    147

7.4.4.1.1    Generation of \(r\text{ZC},m(n)\)    147

7.4.4.1.2    Generation of \(r\text{WUS}(n)\)    148

7.4.4.2    Mapping to physical resources    148

7.4.5    Low-power synchronization signal    148

7.4.5.1    Sequence generation    148

7.4.5.1.1    Generation of \(r\text{OOK}(n)\)    148

7.4.5.1.2    Generation of \(r\text{ZC}(n)\)    149

7.4.5.1.3    Generation of \(r\text{LPSS}(n)\)    149

7.4.5.2    Mapping to physical resources    150

8    Sidelink    150

8.1    Overview    150

8.1.1    Overview of physical channels    150

8.1.2    Overview of physical signals    150

8.2    Physical resources    150

8.2.1    General    150

8.2.2    Numerologies    150

8.2.3    Frame structure    151

8.2.3.1    Frames and subframes    151

8.2.3.2    Slots    151

8.2.4    Antenna ports    151

8.2.5    Resource grid    151

8.2.6    Resource elements    152

8.2.7    Resource blocks    152

8.2.8    Bandwidth part    152

8.3    Physical channels    152

8.3.1    Physical sidelink shared channel    152

8.3.1.1    Scrambling    152

8.3.1.2    Modulation    153

8.3.1.3    Layer mapping    153

8.3.1.4    Precoding    153

8.3.1.5    Mapping to virtual resource blocks    153

8.3.1.6    Mapping from virtual to physical resource blocks    154

8.3.2    Physical sidelink control channel    154

8.3.2.1    Scrambling    154

8.3.2.2    Modulation    154

8.3.2.3    Mapping to physical resources    154

8.3.3    Physical sidelink broadcast channel    154

8.3.3.1    Scrambling    154

8.3.3.2    Modulation    155

8.3.3.3    Mapping to physical resources    155

8.3.4    Physical sidelink feedback channel    155

8.3.4.1    General    155

8.3.4.2    PSFCH format 0    155

8.3.4.2.1    Sequence generation    155

8.3.4.2.2    Mapping to physical resources    155

8.4    Physical signals    156

8.4.1    Reference signals    156

8.4.1.1    Demodulation reference signals for PSSCH    156

8.4.1.1.1    Sequence generation    156

8.4.1.1.2    Mapping to physical resources    156

8.4.1.2    Phase-tracking reference signals for PSSCH    157

8.4.1.2.1    Sequence generation    157

8.4.1.2.2    Mapping to physical resources    157

8.4.1.3    Demodulation reference signals for PSCCH    158

8.4.1.3.1    Sequence generation    158

8.4.1.3.2    Mapping to physical resources    159

8.4.1.4    Demodulation reference signals for PSBCH    159

8.4.1.4.1    Sequence generation    159

8.4.1.4.2    Mapping to physical resources    159

8.4.1.5    CSI reference signals    160

8.4.1.5.1    General    160

8.4.1.5.2    Sequence generation    160

8.4.1.5.3    Mapping to physical resources    160

8.4.1.6    Positioning reference signals    160

8.4.1.6.1    General    160

8.4.1.6.2    Sequence generation    160

8.4.1.6.3    Mapping to physical resources    161

8.4.2    Synchronization signals    162

8.4.2.1    Physical-layer sidelink synchronization identities    162

8.4.2.2    Sidelink primary synchronization signal    162

8.4.2.2.1    Sequence generation    162

8.4.2.2.2    Mapping to physical resources    162

8.4.2.3    Sidelink secondary synchronization signal    162

8.4.2.3.1    Sequence generation    162

8.4.2.3.2    Mapping to physical resources    162

8.4.3    S-SS/PSBCH block    163

8.4.3.1    Time-frequency structure of an S-SS/PSBCH block    163

8.4.3.1.1    Mapping of S-PSS within an S-SS/PSBCH block    163

8.4.3.1.2    Mapping of S-SSS within an S-SS/PSBCH block    163

8.4.3.1.3    Mapping of PSBCH and DM-RS within an S-SS/PSBCH block    163

8.4.3.2    Time location of an S-SS/PSBCH block    164

8.5    Timing    164

Annex A (informative):    Change history    165

 

<br>Foreword #

This Technical Specification has been produced by the 3rd Generation Partnership Project (3GPP).

The contents of the present document are subject to continuing work within the TSG and may change following formal TSG approval. Should the TSG modify the contents of the present document, it will be re-released by the TSG with an identifying change of release date and an increase in version number as follows:

Version x.y.z

where:

x    the first digit:

1    presented to TSG for information;

2    presented to TSG for approval;

3    or greater indicates TSG approved document under change control.

y    the second digit is incremented for all changes of substance, i.e. technical enhancements, corrections, updates, etc.

z    the third digit is incremented when editorial only changes have been incorporated in the document.

<br>1     Scope #

The present document describes the physical channels and signals for 5G-NR.

2     References #

The following documents contain provisions which, through reference in this text, constitute provisions of the present document.

[1]    3GPP TR 21.905: "Vocabulary for 3GPP Specifications".

[2]    3GPP TS 38.201: "NR; Physical Layer – General Description"

[3]    3GPP TS 38.202: "NR; Services provided by the physical layer"

[4]    3GPP TS 38.212: "NR; Multiplexing and channel coding"

[5]    3GPP TS 38.213: "NR; Physical layer procedures for control "

[6]    3GPP TS 38.214: "NR; Physical layer procedures for data "

[7]    3GPP TS 38.215: "NR; Physical layer measurements"

[8]    3GPP TS 38.104: "NR; Base Station (BS) radio transmission and reception"

[9]    void

[10]    3GPP TS 38.306: "NR; User Equipment (UE) radio access capabilities"

[11]    3GPP TS 38.321: "NR; Medium Access Control (MAC) protocol specification"

[12]    3GPP TS 38.133: "NR; Requirements for support of radio resource management"

[13]    3GPP TS 38.304: "NR; User Equipment (UE) procedures in Idle mode and RRC Inactive state"

[14]    3GPP TS 38.101-1: "NR; User Equipment (UE) radio transmission and reception; Part 1: Range 1 Standalone"

[15]    3GPP TS 38.101-2: "NR; User Equipment (UE) radio transmission and reception; Part 2: Range 2 Standalone"

[16]    3GPP TS 38.101-5: "NR; User Equipment (UE) radio transmission and reception; Part 5: Satellite access Radio Frequency (RF) and performance requirements"

[17]    3GPP TS 38.108: "Satellite Access Node radio transmission and reception"

 

 

3     Definitions of terms, symbols and abbreviations #

3.1     Terms #

For the purposes of the present document, the following definitions apply:

3.2     Symbols #

For the purposes of the present document, the following symbols apply:

\((k,l)_{p,\mu}\)    Resource element with frequency-domain index \(k\) and time-domain index \(l\) for antenna port \(p\) and subcarrier spacing configuration \(\mu\); see clause 4.4.3

\(a_{k,l}^{(p,\mu)}\)    Value of resource element \((k,l)\) for antenna port\(p\) and subcarrier spacing configuration \(\mu\); see clause 4.4.3

\(\beta\)    Amplitude scaling for a physical channel/signal

\(c(n)\)    PN sequence; see clause 5.2.1

\(\Delta f\)    Subcarrier spacing

\(\Delta f_{\mathrm{RA}}\)    Subcarrier spacing for random-access preambles

\(\kappa\)    The ratio between \(T_s\) and \(T_c\); see clause 4.1

\(k\)    Subcarrier index relative to a reference

\(l\)    OFDM symbol index relative to a reference

\(\mu\)    Subcarrier spacing configuration, \(\Delta f = 2^{\mu} \bullet 15\lbrack kHz\rbrack\)

\(M_{\text{bit}}^{\text{(}q\text{)}}\)    Number of coded bits to transmit on a physical channel [for codeword \(q\)]

\(M_{\text{symb}}^{\text{(}q\text{)}}\)    Number of modulation symbols to transmit on a physical channel [for codeword \(q\)]

\(M_{\text{symb}}^{\text{layer}}\)    Number of modulation symbols to transmit per layer for a physical channel

\(M_{\text{sc}}^{\text{PUSCH}}\)    Scheduled bandwidth for uplink transmission, expressed as a number of subcarriers

\(M_{\text{RB}}^{\text{PUSCH}}\)    Scheduled bandwidth for uplink transmission, expressed as a number of resource blocks

\(M_{\text{symb}}^{\text{ap}}\)    Number of modulation symbols to transmit per antenna port for a physical channel

\(\nu\)    Number of transmission layers

\(N_{\text{BWP,}i}^{\text{size}}\)    Size of bandwidth part \(i\); see clause 4.4.4.4

\(N_{\text{BWP,}i}^{\text{start}}\)    Start of bandwidth part \(i\); see clause 4.4.4.4

\(N_{\text{CP,}l}^{\mu}\)    Cyclic prefix length; see clause 5.3.1

\(N_{\text{grid,}x}^{\text{size,}\mu}\)    The size of the resource grid; see clauses 4.4.2 and 5.3

\(N_{\text{grid,}x}^{\text{start,}\mu}\)    The start of the resource grid; see clause 4.4.2

\(N_{\text{group}}^{\text{PT-RS}}\)    The number of PT-RS groups; see clause 6.3.1.4

\(N_{\text{ID}}^{\text{cell}}\)    Physical layer cell identity; see clause 7.4.2.1

\(N_{\text{ID}}^{\text{SL}}\)    Physical-layer sidelink identity; see clause 8.4.2.1

\(N_{\text{RB}}^{\text{CORESET}}\)    Frequency-domain size of a control resource set; see clause 7.3.2.2

\(N_{\text{REG}}^{\text{CORESET}}\)    Number of resource-element groups in a CORESET; see clause 7.3.2.2

\(N_{\text{samp}}^{\text{group}}\)    Number of samples per PT-RS group; see clause 6.3.1.4

\(N_{\text{sc}}^{\text{RB}}\)    Number of subcarriers per resource block, see clause 4.4.4.1

\(N_{\text{slot}}^{\text{subframe,}\mu}\)    Number of slots per subframe for subcarrier spacing configuration \(\mu\), see clause 4.3.2

\(N_{\text{slot}}^{\text{frame,}\mu}\)    Number of slots per frame for subcarrier spacing configuration \(\mu\), see clause 4.3.2

\(N_{\text{symb}}^{\text{CORESET}}\)    Time duration of a control resource set; see clause 7.3.2.2

\(N_{\text{symb}}^{\text{PUCCH}}\)    Length of the PUCCH transmission in OFDM symbols; see clause 6.3.2.1

\(N_{\text{symb}}^{\text{subframe,}\mu}\)    Number of OFDM symbols per subframe for subcarrier spacing configuration \(\mu\); see clause 4.3.1

\(N_{\text{symb}}^{\text{slot}}\)    Number of symbols per slot

\(N_{\text{TA}}\)    Timing advance between downlink and uplink; see clause 4.3.1

\(N_{\text{TA,offset}}\)    A fixed offset used to calculate the timing advance; see clause 4.3.1

\(N_{\text{TA,adj}}^{\text{common}}\)    Network-controlled timing correction; see clause 4.3.1

\(N_{\text{TA,adj}}^{\text{UE}}\)    UE-derived timing correction; see clause 4.3.1

\(N_{\text{Rx-Tx}}\)    Minimum time from reception to transmission for a half-duplex UE; see clause 4.3.2

\(n_{\text{f}}\)    System frame number (SFN)

\(n_{\text{CRB}}^{\mu}\)    Common resource block number for subcarrier spacing configuration \(\mu\), see clause 4.4.4.3

\(n_{\text{HFN}}\)    Hyper-frame number

\(n_{\text{PRB}}\)    Physical resource block number; see clause 4.4.4.4

\(n_{\text{RNTI}}\)    Radio network temporary identifier

\(n_{\text{s}}^{\mu}\)    Slot number within a subframe for subcarrier spacing configuration \(\mu\); see clause 4.3.2

\(n_{\text{s,f}}^{\mu}\)    Slot number within a frame for subcarrier spacing configuration \(\mu\); see clause 4.3.2

\(p\)    Antenna port number

\(Q_m\)    Modulation order

\(\rho\)    Number of antenna ports

\({\bar{r}}_{u,v}(n)\)    Low-PAPR base sequence; see clause 5.2.2

\(r_{u,v}^{(\alpha,\delta)}(n)\)    Low-PAPR sequence; see clause 5.2.2

\(s_{l}^{({p,\mu})}(t)\)    The time-continuous signal on antenna port \(p\) and subcarrier spacing configuration \(\mu\) for OFDM symbol \(l\) in a subframe; see clause 5.3.1

\(T_c\)    Basic time unit for NR; see clause 4.1

\(T_f\)    Radio frame duration; see clause 4.3.1

\(T_s\)    Basic time unit for LTE

\(T_{sf}\)    Subframe duration; see clause 4.3.1

\(T_{\mathrm{slot}}\)    Slot duration; see clause 4.3.2

\(T_{TA}\)    Timing advance between downlink and uplink; see clause 4.3.1

\(W\)    Precoding matrix for spatial multiplexing

 

3.3     Abbreviations #

For the purposes of the present document, the following abbreviations apply:

BWP    Bandwidth Part

CCE    Control Channel Element

CORESET    Control Resource Set

CRB    Common Resource Block

CSI    Channel-State Information

CSI-RS    CSI Reference Signal

DCI    Downlink Control Information

DM-RS    Demodulation Reference Signal

FR1    Frequency Range 1 as defined in TS 38.104 [8]

FR2    Frequency Range 2 as defined in TS 38.104 [8]

FR2-NTN    Frequency Range 2 for Non-terrestrial networks as defined in TS 38.101-5 [16]

IAB    Integrated Access and Backhaul

IAB-MT    IAB Mobile Termination

IE    Information Element

NCR    Network-Controlled repeater

NCR-MT    NCR Mobile Termination

PBCH    Physical Broadcast Channel

PDCCH    Physical Downlink Control Channel

PDSCH    Physical Downlink Shared Channel

PRACH    Physical Random-Access Channel

PRB    Physical Resource Block

PSS    Primary Synchronization Signal

PT-RS    Phase-tracking reference signal

PUCCH    Physical Uplink Control Channel

PUSCH    Physical Uplink Shared Channel

RAR    Random Access Response

REG    Resource-Element Group

RIM    Remote Interference Management

RIM-RS    Remote Interference Management Reference Signal

SRS    Sounding Reference Signal

SSS    Secondary Synchronization Signal

VRB    Virtual Resource Block

 

4     Frame structure and physical resources #

4.1     General #

Throughout this specification, unless otherwise noted, the size of various fields in the time domain is expressed in time units \(T_c = \frac{1}{\Delta f_{\max} \cdot N_f}\) where \(\Delta f_{\max} = 480 \bullet 10^{3}\) Hz and \(N_f = 4096\). The constant \(\kappa = T_s/T_c = 64\) where \(T_s=\frac{1}{\Delta f_{\mathrm{ref}}\cdot N_{f,\mathrm{ref}}}\), \(\Delta f_{\mathrm{ref}} = 15 \cdot 10^{3}\ \mathrm{Hz}\) and \(N_{f,\mathrm{ref}} = 2048\).

Throughout this specification, unless otherwise noted, statements using the term "UE" in clauses 4, 5, 6, or 7 are equally applicable to the IAB-MT part of an IAB-node and the NCR-MT part of an NCR node.

4.2     Numerologies #

Multiple OFDM numerologies are supported as given by Table 4.2-1 where \(\mu\) and the cyclic prefix for a downlink or uplink bandwidth part are obtained from the higher-layer parameters subcarrierSpacing and cyclicPrefix, respectively.

Table 4.2-1: Supported transmission numerologies.

\(\mu\)

\(\Delta f = 2^{\mu} \cdot 15\,[\mathrm{kHz}]\)

Cyclic prefix

0

15

Normal

1

30

Normal

2

60

Normal, Extended

3

120

Normal

4

240

Normal

5

480

Normal

6

960

Normal

 

4.3     Frame structure #

4.3 .1    Frames and subframes #

Downlink, uplink, and sidelink transmissions are organized into frames with \(T_f = \left(\frac{\Delta f_{\max} N_f}{100}\right)\cdot T_c = 10\,\mathrm{ms}\) duration, each consisting of ten subframes of \(T_{sf} = \left( \Delta f_{\max} N_f / 1000 \right) \cdot T_c = 1\,\mathrm{ms}\) duration. The number of consecutive OFDM symbols per subframe is \(N_{\text{symb}}^{\text{subframe},\mu} = N_{\text{symb}}^{\text{slot}}N_{\text{slot}}^{\text{subframe},\mu}\). Each frame is divided into two equally-sized half-frames of five subframes each with half-frame 0 consisting of subframes 0 – 4 and half-frame 1 consisting of subframes 5 – 9.

There is one set of frames in the uplink and one set of frames in the downlink on a carrier.

Uplink frame number \(i\) for transmission from the UE shall start \(T_{\text{TA}} = \left( {N_{\text{TA}} + N_{\text{TA,offset}} + N_{\text{TA,adj}}^{\text{common}} + N_{\text{TA,adj}}^{\text{UE}}} \right)T_{\text{c}}\) before the start of the corresponding downlink frame at the UE where

- \(N_{\text{TA}}\) and \(N_{\text{TA,offset}}\) are given by clause 4.2 of [5, TS 38.213], except for msgA transmission on PUSCH where \(N_{\text{TA}} = 0\) shall be used;

-    \(N_{\text{TA,adj}}^{\text{common}}\) given by clause 4.2 of [5, TS 38.213] is derived from the higher-layer parameters ta-Common, ta-CommonDrift, and ta-CommonDriftVariant if configured, otherwise \(N_{\text{TA,adj}}^{\text{common}} = 0\);

-    \(N_{\text{TA,adj}}^{\text{UE}}\) given by clause 4.2 of [5, TS 38.213] is computed by the UE based on UE position and serving-satellite-ephemeris-related higher-layers parameters if configured, or is computed by the UE based on UE position and gNB location provided by atg-gNB-Location if configured, otherwise \(N_{\text{TA,adj}}^{\text{UE}} = 0\).

 

Image

Figure 4.3.1-1: Uplink-downlink timing relation.

 

4.3 .2    Slots #

For subcarrier spacing configuration \(\mu\), slots are numbered \(n_{\text{s}}^{\mu} \in \left\{ {0,\ldots,N_{\text{slot}}^{\text{subframe},\mu} - 1} \right\}\) in increasing order within a subframe and \(n_{\text{s,f}}^{\mu} \in \left\{ {0,\ldots,N_{\text{slot}}^{\text{frame},\mu} - 1} \right\}\) in increasing order within a frame. There are \(N^{\text{slot}}_{\text{symb}}\) consecutive OFDM symbols in a slot where \(N^{\text{slot}}_{\text{symb}}\) depends on the cyclic prefix as given by Tables 4.3.2-1 and 4.3.2-2. The start of slot \(n_{\text{s}}^{\mu}\) in a subframe is aligned in time with the start of OFDM symbol \(n_{s}^{\mu} N_{\text{symb}}^{\text{slot}}\) in the same subframe.

OFDM symbols in a slot in a downlink or uplink frame can be classified as 'downlink', 'flexible', or 'uplink'. Signaling of slot formats is described in clause 11.1 of [5, TS 38.213].

In a slot in a downlink frame, the UE shall assume that downlink transmissions only occur in 'downlink' or 'flexible' symbols.

In a slot in an uplink frame, the UE shall only transmit in 'uplink' or 'flexible' symbols.

A UE not capable of full-duplex communication and not supporting simultaneous transmission and reception as defined by parameter simultaneousRxTxInterBandENDC, simultaneousRxTxInterBandCA or simultaneousRxTxSUL [10, TS 38.306] among all cells within a group of cells is not expected to transmit in the uplink in one cell within the group of cells earlier than \(N_{\text{Rx-Tx}}T_{\text{c}}\) after the end of the last received downlink symbol in the same or different cell within the group of cells where \(N_{\text{Rx-Tx}}\) is given by Table 4.3.2-3.

A UE not capable of full-duplex communication and not supporting simultaneous transmission and reception as defined by parameter simultaneousRxTxInterBandENDC, simultaneousRxTxInterBandCA or simultaneousRxTxSUL [10, TS 38.306] among all cells within a group of cells is not expected to receive in the downlink in one cell within the group of cells earlier than \(N_{\text{Tx-Rx}}T_{\text{c}}\) after the end of the last transmitted uplink symbol in the same or different cell within the group of cells where \(N_{\text{Tx-Rx}}\) is given by Table 4.3.2-3.

For DAPS handover operation, a UE not capable of full-duplex communication is not expected to transmit in the uplink to a cell earlier than \(N_{\text{Rx-Tx}}T_{\text{c}}\) after the end of the last received downlink symbol in the different cell where \(N_{\text{Rx-Tx}}\) is given by Table 4.3.2-3.

For DAPS handover operation, a UE not capable of full-duplex communication is not expected to receive in the downlink from a cell earlier than \(N_{\text{Tx-Rx}}T_{\text{c}}\) after the end of the last transmitted uplink symbol in the different cell where \(N_{\text{Tx-Rx}}\) is given by Table 4.3.2-3.

A UE not capable of full-duplex communication is not expected to transmit in the uplink earlier than \(N_{\text{Rx-Tx}}T_{\text{c}}\) after the end of the last received downlink symbol in the same cell where \(N_{\text{Rx-Tx}}\) is given by Table 4.3.2-3.

A UE not capable of full-duplex communication is not expected to receive in the downlink earlier than \(N_{\text{Tx-Rx}}T_{\text{c}}\) after the end of the last transmitted uplink symbol in the same cell where \(N_{\text{Tx-Rx}}\) is given by Table 4.3.2-3.

Table 4.3.2-1: Number of OFDM symbols per slot, slots per frame, and slots per subframe for normal cyclic prefix.

\[\mathbf{\mu}\]

\[\mathbf{N}_{\text{symb}}^{\text{slot}}\]

\[\mathbf{N}_{\text{slot}}^{\text{frame},\mathbf{\mu}}\]

\[\mathbf{N}_{\text{slot}}^{\text{subframe},\mathbf{\mu}}\]

0

14

10

1

1

14

20

2

2

14

40

4

3

14

80

8

4

14

160

16

5

14

320

32

6

14

640

64

 

Table 4.3.2-2: Number of OFDM symbols per slot, slots per frame, and slots per subframe for extended cyclic prefix.

\[\mathbf{\mu}\]

\[\mathbf{N}_{\text{symb}}^{\text{slot}}\]

\[\mathbf{N}_{\text{slot}}^{\text{frame},\mathbf{\mu}}\]

\[\mathbf{N}_{\text{slot}}^{\text{subframe},\mathbf{\mu}}\]

2

12

40

4

 

Table 4.3.2-3: Transition time \(\mathbf{N}_{\text{Rx-Tx}}\) and \(\mathbf{N}_{\text{Tx-Rx}}\)

Transition time

FR1

FR2

\[N_{\text{Tx-Rx}}\]

25600

13792

\[N_{\text{Rx-Tx}}\]

25600

13792

 

4.4     Physical resources #

4.4 .1    Antenna ports #

An antenna port is defined such that the channel over which a symbol on the antenna port is conveyed can be inferred from the channel over which another symbol on the same antenna port is conveyed.

Two antenna ports are said to be quasi co-located if the large-scale properties of the channel over which a symbol on one antenna port is conveyed can be inferred from the channel over which a symbol on the other antenna port is conveyed. The large-scale properties include one or more of delay spread, Doppler spread, Doppler shift, average gain, average delay, and spatial Rx parameters.

4.4 .2    Resource grid #

For each numerology and carrier, a resource grid of \(N_{grid,x}^{size,\mu}\, N_{sc}^{RB}\) subcarriers and \(N_{\text{symb}}^{\text{subframe},\mu}\) OFDM symbols is defined, starting at common resource block \(N^{\text{start},\mu}_{\text{grid}}\) indicated by higher-layer signalling. There is one set of resource grids per transmission direction (uplink, downlink, or sidelink) with the subscript\(x\) set to DL, UL, and SL for downlink, uplink, and sidelink, respectively. When there is no risk for confusion, the subscript \(x\) may be dropped. There is one resource grid for a given antenna port \(p\), subcarrier spacing configuration \(\mu\), and transmission direction (downlink, uplink, or sidelink).

For uplink and downlink, the carrier bandwidth \(N_{\text{grid}}^{\text{size},\mu}\) for subcarrier spacing configuration \(\mu\) is given by the higher-layer parameter carrierBandwidth in the SCS-SpecificCarrier IE. The starting position \(N_{\text{grid}}^{\text{start},\mu}\) for subcarrier spacing configuration \(\mu\) is given by the higher-layer parameter offsetToCarrier in the SCS-SpecificCarrier IE.

The frequency location of a subcarrier refers to the center frequency of that subcarrier.

For the downlink, the higher-layer parameter txDirectCurrentLocation in the SCS-SpecificCarrier IE indicates the location of the transmitter DC subcarrier in the downlink for each of the numerologies configured in the downlink. Values in the range 0 – 3299 represent the number of the DC subcarrier and the value 3300 indicates that the DC subcarrier is located outside the resource grid.

For the uplink, the higher-layer parameter txDirectCurrentLocation in the UplinkTxDirectCurrentBWP IE indicates the location of the transmitter DC subcarrier in the uplink for each of the configured bandwidth parts, including whether the DC subcarrier location is offset by 7.5 kHz relative to the center of the indicated subcarrier or not. Values in the range 0 – 3299 represent the number of the DC subcarrier, the value 3300 indicates that the DC subcarrier is located outside the resource grid, and the value 3301 indicates that the position of the DC subcarrier in the uplink is undetermined.

4.4 .3    Resource elements #

Each element in the resource grid for antenna port \(p\) and subcarrier spacing configuration \(\mu\) is called a resource element and is uniquely identified by \((k,l)_{p,\mu}\) where \(k\) is the index in the frequency domain and \(\ell\) refers to the symbol position in the time domain relative to some reference point. Resource element \((k,l)_{p,\mu}\) corresponds to a physical resource and the complex value \(a_{k,l}^{(p,\mu)}\). When there is no risk for confusion, or no particular antenna port or subcarrier spacing is specified, the indices \(p\) and \(\mu\) may be dropped, resulting in \(a_{k,l}^{(p)}\) or \(a_{k,l}\).

4.4 .4    Resource blocks #

4.4.4.1     General #

A resource block is defined as \(N_{\text{sc}}^{\text{RB}} = 12\) consecutive subcarriers in the frequency domain.

4.4.4.2     Point A #

Point A serves as a common reference point for resource block grids and is obtained from:

-    offsetToPointA for a PCell downlink where offsetToPointA represents the frequency offset between point A and the lowest subcarrier of the lowest resource block, which overlaps with the SS/PBCH block, or the SS/PBCH block after puncturing if applicable, used by the UE for initial cell selection, expressed in units of resource blocks assuming 15 kHz subcarrier spacing for FR1 and 60 kHz subcarrier spacing for FR2 and FR2-NTN;

-    for operation without shared spectrum channel access in FR1, FR2-1 and FR2-NTN, the lowest resource block has the subcarrier spacing provided by the higher layer parameter subCarrierSpacingCommon;

-    for operation with shared spectrum channel access in FR1 or FR2, and for operation without shared spectrum channel access in FR2-2, the lowest resource block has the subcarrier spacing same as the SS/PBCH block used by the UE for initial cell selection;

-    absoluteFrequencyPointA for all other cases where absoluteFrequencyPointA represents the frequency-location of point A expressed as in ARFCN.

4.4.4. 3    Common resource blocks #

Common resource blocks are numbered from 0 and upwards in the frequency domain for subcarrier spacing configuration \(\mu\). The center of subcarrier 0 of common resource block 0 for subcarrier spacing configuration \(\mu\) coincides with 'point A'.

The relation between the common resource block number \(n_{\text{CRB}}^{\mu}\) in the frequency domain and resource elements \((k,l)\) for subcarrier spacing configuration \(\mu\) is given by

    \(n_{\mathrm{CRB}}^{\mu} = \left\lfloor \frac{k}{N_{sc}^{\mathrm{RB}}} \right\rfloor\)

where \(k\) is defined relative to point A such that \(k = 0\) corresponds to the subcarrier centered around point A.

4.4.4. 4    Physical resource blocks #

Physical resource blocks for subcarrier spacing configuration \(\mu\) are defined within a bandwidth part and numbered from 0 to \(N_{\text{BWP},i}^{\text{size,μ}} - 1\) where \(i\) is the number of the bandwidth part. The relation between the physical resource block \(n_{\text{PRB}}^{\mu}\) in bandwidth part \(i\) and the common resource block \(n_{\text{CRB}}^{\mu}\) is given by

\[n_{\text{CRB}}^{\mu} = n_{\text{PRB}}^{\mu} + N_{\text{BWP},i}^{\text{start,μ}}\]

where \(N_{\text{BWP},i}^{\text{start,}\mu}\) is the common resource block where bandwidth part \(i\) starts relative to common resource block 0. When there is no risk for confusion the index \(\mu\) may be dropped.

4.4.4. 5    Virtual resource blocks #

Virtual resource blocks are defined within a bandwidth part and numbered from 0 to \(N_{\text{BWP},i}^{\text{size}} - 1\) where \(i\) is the number of the bandwidth part.

4.4.4.6     Interlaced resource blocks #

Multiple interlaces of resource blocks are defined where interlace \(m \in \left\{ {0,1,\ldots,M - 1} \right\}\) consists of common resource blocks \(\left\{ {m,M + m,2M + m,3M + m,\ldots} \right\}\), with \(M\) being the number of interlaces given by Table 4.4.4.6-1. The relation between the interlaced resource block \(n_{\text{IRB},m}^{\mu} \in \left\{ {0,1,\ldots} \right\}\) in bandwidth part \(i\) and interlace \(m\) and the common resource block \(n_{\text{CRB}}^{\mu}\) is given by

\[n_{\text{CRB}}^{\mu} = Mn_{\text{IRB},m}^{\mu} + N_{\text{BWP},i}^{\text{start,μ}} + \left( {\left( {m - N_{\text{BWP},i}^{\text{start,μ}}} \right)\text{mod}M} \right)\]

where \(N_{\text{BWP},i}^{\text{start,}\mu}\) is the common resource block where bandwidth part starts relative to common resource block 0. When there is no risk for confusion the index \(\mu\) may be dropped.

The UE expects that the number of common resource blocks in an interlace contained within bandwidth part \(i\) is no less than 10.

Table 4.4.4.6-1: The number of resource block interlaces.

\[\mathbf{\mu}\]

\[\mathbf{M}\]

0

10

1

5

 

4.4 .5    Bandwidth part #

A bandwidth part is a subset of contiguous common resource blocks defined in clause 4.4.4.3 for a given numerology \(\mu_i\) in bandwidth part \(i\) on a given carrier. The starting position \(N_{\text{BWP},i}^{\text{start,}\mu}\) and the number of resource blocks \(N_{\text{BWP},i}^{\text{size,}\mu}\) in a bandwidth part shall fulfil \(N_{\text{grid},x}^{\text{start},\mu} \leq N_{\text{BWP},i}^{\text{start},\mu} < N_{\text{grid},x}^{\text{start},\mu} + N_{\text{grid},x}^{\text{size},\mu}\) and \(N_{\text{grid},x}^{\text{start},\mu} < N_{\text{BWP},i}^{\text{start},\mu} + N_{\text{BWP},i}^{\text{size},\mu} \leq N_{\text{grid},x}^{\text{start},\mu} + N_{\text{grid},x}^{\text{size},\mu}\), respectively. Configuration of a bandwidth part is described in clause 12 of [5, TS 38.213].

A UE can be configured with up to four bandwidth parts in the downlink with a single downlink bandwidth part being active at a given time. The UE is not expected to receive PDSCH, PDCCH, or CSI-RS (except for RRM) outside an active bandwidth part.

A UE can be configured with up to four bandwidth parts in the uplink with a single uplink bandwidth part being active at a given time. If a UE is configured with a supplementary uplink, the UE can in addition be configured with up to four bandwidth parts in the supplementary uplink with a single supplementary uplink bandwidth part being active at a given time. The UE shall not transmit PUSCH or PUCCH outside an active bandwidth part. For an active cell, the UE shall not transmit SRS configured by SRS-Resource outside an active bandwidth part.

Unless otherwise noted, the description in this specification applies to each of the bandwidth parts. When there is no risk of confusion, the index \(\mu\) may be dropped from \(N_{\text{BWP},i}^{\text{start},\mu}\), \(N_{\text{BWP},i}^{\text{size},\mu}\), \(N_{\text{grid},x}^{\text{start},\mu}\), and \(N_{\text{grid},x}^{\text{size},\mu}\).

4.4.6     Common MBS frequency resource #

A common MBS frequency resource is a contiguous set of common resource blocks. The starting position \(N_{\text{MBS},i}^{\text{start,}\mu}\) of the common MBS frequency resource \(i\) is defined relative to point A and the size of the common MBS frequency resource is given by \(N_{\text{MBS},i}^{\text{size,}\mu}\). Resource blocks in a common MBS frequency resource are numbered in the same way as resource blocks in clause 4.4.4.4 with \(N_{\text{BWP},i}^{\text{start,μ}}\) and \(N_{\text{BWP},i}^{\text{size,μ}}\) replaced by \(N_{\text{MBS},i}^{\text{start,}\mu}\) and \(N_{\text{MBS},i}^{\text{size,}\mu}\), respectively.

A UE is not expected to receive PDSCH or PDCCH associated with MBS transmissions scheduled with G-RNTI, G-CS-RNTI, MCCH-RNTI, or Multicast-MCCH-RNTI outside the common MBS frequency resource.

4.5     Carrier aggregation #

Transmissions in multiple="multiple" cells can be aggregated. Unless otherwise noted, the description in this specification applies to each of the serving cells.

For carrier aggregation of cells with unaligned frame boundaries, the slot offset \(N_{\text{slot, offset}}^{\text{CA}}\) between a PCell/PScell and an SCell is determined by higher-layer parameter ca-SlotOffset for the SCell. The quantity \(\mu_{\text{offset}}\) is defined as the maximum of the lowest subcarrier spacing configuration among the subcarrier spacings given by the higher-layer parameters scs-SpecificCarrierList configured for PCell/PSCell and the SCell, respectively. The slot offset \(N_{\text{slot, offset}}^{\text{CA}}\) fulfills

-    when the lowest subcarrier spacing configuration among the subcarrier spacings configured for the cell is \(\mu = 2\) for both cells or \(\mu = 3\) for both cells, the start of slot 0 for the cell whose point A has a lower frequency coincides with the start of slot \({qN}_{\text{slot, offset}}^{\text{CA}}\text{mod}N_{\text{slot}}^{\text{frame},\mathbf{\mu}_{\text{offset}}}\) for the other cell where \(q = - 1\) if point A of the PCell/PSCell has a frequency lower than the frequency of point A for the SCell, otherwise \(q = 1\);

-    otherwise, the start of slot 0 for the cell with the lower subcarrier spacing of the lowest subcarrier spacing given by the higher-layer parameters scs-SpecificCarrierList configured for the two cells, or the Pcell/PSCell if both cells have the same lowest subcarrier spacing given by the higher-layer parameters scs-SpecificCarrierList configured for the two cells, coincides with the start of slot \({qN}_{\text{slot, offset}}^{\text{CA}}\text{mod}N_{\text{slot}}^{\text{frame},\mathbf{\mu}_{\text{offset}}}\) for the other cell where \(q = - 1\) if the lowest subcarreier spacing configuration given by scs-SpecificCarrierList of the PCell/PSCell is smaller than or equal to the lowest subcarrier spacing given by scs-SpecificCarrierList for the SCell, otherwise \(q = 1\).

 

5     Generic functions #

5.1     Modulation mapper #

The modulation mapper takes binary digits, 0 or 1, as input and produces complex-valued modulation symbols as output.

5.1.1     π/2-BPSK #

In case of π/2-BPSK modulation, bit \(b(i)\) is mapped to complex-valued modulation symbol \(d(i)\) according to

    \(d(i)=\frac{e^{\frac{j\pi}{2}(i \bmod 2)}}{\sqrt{2}}\left[(1-2b(i))+j(1-2b(i))\right]\)

5.1.2     BPSK #

In case of BPSK modulation, bit \(b(i)\) is mapped to complex-valued modulation symbol \(d(i)\) according to

    \(d(i)=\frac{1}{\sqrt{2}}\left[(1-2b(i))+j(1-2b(i))\right]\)

5.1.3     QPSK #

In case of QPSK modulation, pairs of bits, \(b(2i),\,b(2i+1)\), are mapped to complex-valued modulation symbols \(d(i)\) according to

    \(d(i)=\frac{1}{\sqrt{2}}\left[(1-2\,b(2i))+j(1-2\,b(2i+1))\right]\)

5.1.4     16QAM #

In case of 16QAM modulation, quadruplets of bits, \(b(4i), b(4i+1), b(4i+2), b(4i+3)\), are mapped to complex-valued modulation symbols \(d(i)\) according to

\(d(i)=\frac{1}{\sqrt{10}}\left\{(1-2b(4i))\left[2-(1-2b(4i+2))\right]+j(1-2b(4i+1))\left[2-(1-2b(4i+3))\right]\right\}\)

5.1.5     64QAM #

In case of 64QAM modulation, hextuplets of bits, \(b(6i), b(6i+1), b(6i+2), b(6i+3), b(6i+4), b(6i+5)\), are mapped to complex-valued modulation symbols \(d(i)\) according to

\(d(i)=\frac{1}{\sqrt{42}}\left\{(1-2b(6i))\left[4-(1-2b(6i+2))\left[2-(1-2b(6i+4))\right]\right]+j(1-2b(6i+1))\left[4-(1-2b(6i+3))\left[2-(1-2b(6i+5))\right]\right]\right\}\)

5.1.6     256QAM #

In case of 256QAM modulation, octuplets of bits, \(b(8i), b(8i+1), b(8i+2), b(8i+3), b(8i+4), b(8i+5), b(8i+6), b(8i+7)\), are mapped to complex-valued modulation symbols \(d(i)\) according to

\(d(i)=\frac{1}{\sqrt{170}}\left\{(1-2b(8i))\Big[8-(1-2b(8i+2))\Big[4-(1-2b(8i+4))\Big[2-(1-2b(8i+6))\Big]\Big]\Big]+j(1-2b(8i+1))\Big[8-(1-2b(8i+3))\Big[4-(1-2b(8i+5))\Big[2-(1-2b(8i+7))\Big]\Big]\Big]\right\}\)

5.1.7     1024QAM #

In case of 1024QAM modulation, 10-tuplets of bits, \(b\left( {10i} \right),b\left( {10i + 1} \right),b\left( {10i + 2} \right),b\left( {10i + 3} \right),b\left( {10i + 4} \right),b\left( {10i + 5} \right),b\left( {10i + 6} \right),b\left( {10i + 7} \right),b\left( {10i + 8} \right),b\left( {10i + 9} \right)\), are mapped to complex-valued modulation symbols \(d(i)\) according to

di=16821-2b10i+016-1-2b10i+28-1-2b10i+44-1-2b10i+62-1-2b10i+8+j16821-2b10i+116-1-2b10i+38-1-2b10i+54-1-2b10i+72-1-2b10i+9

5.2     Sequence generation #

5.2.1     Pseudo-random sequence generation #

Generic pseudo-random sequences are defined by a length-31 Gold sequence. The output sequence \(c(n)\) of length\(M_{PN}\), where\(n=0,1,\ldots,M_{PN}-1\), is defined by

\(\[ \begin{aligned} c(n)&=(x_1(n+N_c)+x_2(n+N_c))\bmod 2\\ x_1(n+31)&=(x_1(n+3)+x_1(n))\bmod 2\\ x_2(n+31)&=(x_2(n+3)+x_2(n+2)+x_2(n+1)+x_2(n))\bmod 2 \end{aligned} \]\)

where \(N_{\text{C}} = 1600\) and the first m-sequence \(x_{1}(n)\) shall be initialized with\(x_{1}(0)=1,\; x_{1}(n)=0,\; n=1,2,\ldots,30\). The initialization of the second m-sequence, \(x_{2}(n)\), is denoted by \(c_{\text{init}} = \sum_{i=0}^{30} x_2(i)\cdot 2^i\) with the value depending on the application of the sequence.

5.2.2     Low-PAPR sequence generation type 1 #

The low-PAPR sequence \(r_{u,v}^{(\alpha,\delta)}(n)\) is defined by a cyclic shift \(\alpha\) of a base sequence \(\bar{r}_{u,v}(n)\) according to

\(r_{u,v}^{(a,\delta)}(n)=e^{j a n}\,\bar{r}_{u,v}(n),\quad 0\le n<M_{ZC}\)

where \(M_{\text{ZC}} = {{mN_{\text{sc}}^{\text{RB}}}/2^{\delta}}\) is the length of the sequence. Multiple sequences are defined from a single base sequence through different values of \(\alpha\) and \(\delta\).

Base sequences \(\bar{r}_{u,v}(n)\) are divided into groups, where \(u \in \{0,1,\ldots,29\}\) is the group number and \(\nu\) is the base sequence number within the group, such that each group contains one base sequence (\(v = 0\)) of each length \(M_{\text{ZC}} = {{mN_{\text{sc}}^{\text{RB}}}/2^{\delta}}\), \(\frac{1}{2} \le \frac{m}{2^{\delta}} \le 5\) and two base sequences (\(v = 0,1\)) of each length \(M_{\text{ZC}} = {{mN_{\text{sc}}^{\text{RB}}}/2^{\delta}}\), \(6 \le \frac{m}{2^8}\). The definition of the base sequence \(\bar{r}_{u,v}(0),\ldots,\bar{r}_{u,v}(M_{ZC}-1)\) depends on the sequence length \(M_{zC}\).

5.2.2.1     Base sequences of length 36 or larger #

For\(M_{\text{ZC}} \geq 3N_{\text{sc}}^{\text{RB}}\), the base sequence \(\bar{r}_{u,v}(0),\ldots,\bar{r}_{u,v}(M_{ZC}-1)\) is given by

\(\bar{r}_{u,v}(n)=x_q\left(n \bmod N_{ZC}\right)\\ x_q(m)=e^{-j\frac{\pi q m(m+1)}{N_{ZC}}}\)

where

\(\begin{aligned} q &= \left[ \bar{q} + \frac{1}{2} \right] + v \cdot (-1)^{\left[2q\right]} \\ \bar{q} &= N_{ZC} \cdot \frac{u+1}{31} \end{aligned}\)

The length \(N_{ZC}\) is given by the largest prime number such that\(N_{ZC} < M_{ZC}\).

5.2.2.2     Base sequences of length less than 36 #

For \(M_{ZC} \in \{6,12,18,24\}\) the base sequence is given by

\(\bar{r}_{u,v}(n)=e^{j\varphi(n)\pi/4},\quad 0\le n\le M_{ZC}-1\)

where the value of \(\varphi(n)\) is given by Tables 5.2.2.2-1 to 5.2.2.2-4.

For \(M_{ZC} = 30\), the base sequence \(\bar{r}_{u,v}(0),\ldots,\bar{r}_{u,v}(M_{ZC}-1)\) is given by

\(\bar{r}_{u,v}(n)=e^{-j\frac{\pi (u+1)(n+1)(n+2)}{31}},\; 0\le n \le M_{ZC}-1\)

 

Table 5.2.2.2-1: Definition of \(\varphi(n)\) for\(M_{zC} = 6\).

\(u\)

\(\varphi(0),\ldots,\varphi(5)\)

0

-3

-1

3

3

-1

-3

1

-3

3

-1

-1

3

-3

2

-3

-3

-3

3

1

-3

3

1

1

1

3

-1

-3

4

1

1

1

-3

-1

3

5

-3

1

-1

-3

-3

-3

6

-3

1

3

-3

-3

-3

7

-3

-1

1

-3

1

-1

8

-3

-1

-3

1

-3

-3

9

-3

-3

1

-3

3

-3

10

-3

1

3

1

-3

-3

11

-3

-1

-3

1

1

-3

12

1

1

3

-1

-3

3

13

1

1

3

3

-1

3

14

1

1

1

-3

3

-1

15

1

1

1

-1

3

-3

16

-3

-1

-1

-1

3

-1

17

-3

-3

-1

1

-1

-3

18

-3

-3

-3

1

-3

-1

19

-3

1

1

-3

-1

-3

20

-3

3

-3

1

1

-3

21

-3

1

-3

-3

-3

-1

22

1

1

-3

3

1

3

23

1

1

-3

-3

1

-3

24

1

1

3

-1

3

3

25

1

1

-3

1

3

3

26

1

1

-1

-1

3

-1

27

1

1

-1

3

-1

-1

28

1

1

-1

3

-3

-1

29

1

1

-3

1

-1

-1

 

 

Table 5.2.2.2-2: Definition of \(\varphi(n)\) for\(M_{zC}=12\).

\[\mathbf{u}\]

\[\mathbf{\varphi}(0),\ldots,\mathbf{\varphi}(11)\]

0

-3

1

-3

-3

-3

3

-3

-1

1

1

1

-3

1

-3

3

1

-3

1

3

-1

-1

1

3

3

3

2

-3

3

3

1

-3

3

-1

1

3

-3

3

-3

3

-3

-3

-1

3

3

3

-3

3

-3

1

-1

-3

4

-3

-1

-1

1

3

1

1

-1

1

-1

-3

1

5

-3

-3

3

1

-3

-3

-3

-1

3

-1

1

3

6

1

-1

3

-1

-1

-1

-3

-1

1

1

1

-3

7

-1

-3

3

-1

-3

-3

-3

-1

1

-1

1

-3

8

-3

-1

3

1

-3

-1

-3

3

1

3

3

1

9

-3

-1

-1

-3

-3

-1

-3

3

1

3

-1

-3

10

-3

3

-3

3

3

-3

-1

-1

3

3

1

-3

11

-3

-1

-3

-1

-1

-3

3

3

-1

-1

1

-3

12

-3

-1

3

-3

-3

-1

-3

1

-1

-3

3

3

13

-3

1

-1

-1

3

3

-3

-1

-1

-3

-1

-3

14

1

3

-3

1

3

3

3

1

-1

1

-1

3

15

-3

1

3

-1

-1

-3

-3

-1

-1

3

1

-3

16

-1

-1

-1

-1

1

-3

-1

3

3

-1

-3

1

17

-1

1

1

-1

1

3

3

-1

-1

-3

1

-3

18

-3

1

3

3

-1

-1

-3

3

3

-3

3

-3

19

-3

-3

3

-3

-1

3

3

3

-1

-3

1

-3

20

3

1

3

1

3

-3

-1

1

3

1

-1

-3

21

-3

3

1

3

-3

1

1

1

1

3

-3

3

22

-3

3

3

3

-1

-3

-3

-1

-3

1

3

-3

23

3

-1

-3

3

-3

-1

3

3

3

-3

-1

-3

24

-3

-1

1

-3

1

3

3

3

-1

-3

3

3

25

-3

3

1

-1

3

3

-3

1

-1

1

-1

1

26

-1

1

3

-3

1

-1

1

-1

-1

-3

1

-1

27

-3

-3

3

3

3

-3

-1

1

-3

3

1

-3

28

1

-1

3

1

1

-1

-1

-1

1

3

-3

1

29

-3

3

-3

3

-3

-3

3

-1

-1

1

3

-3

 

Table 5.2.2.2-3: Definition of \(\varphi(n)\) for \(M_{zC}=18\)

\[\mathbf{u}\]

\[\mathbf{\varphi}(0),\ldots,\mathbf{\varphi}(17)\]

0

-1

3

-1

-3

3

1

-3

-1

3

-3

-1

-1

1

1

1

-1

-1

-1

1

3

-3

3

-1

1

3

-3

-1

-3

-3

-1

-3

3

1

-1

3

-3

3

2

-3

3

1

-1

-1

3

-3

-1

1

1

1

1

1

-1

3

-1

-3

-1

3

-3

-3

3

3

3

1

-3

1

3

3

1

-3

-3

3

-1

-3

-1

1

4

1

1

-1

-1

-3

-1

1

-3

-3

-3

1

-3

-1

-1

1

-1

3

1

5

3

-3

1

1

3

-1

1

-1

-1

-3

1

1

-1

3

3

-3

3

-1

6

-3

3

-1

1

3

1

-3

-1

1

1

-3

1

3

3

-1

-3

-3

-3

7

1

1

-3

3

3

1

3

-3

3

-1

1

1

-1

1

-3

-3

-1

3

8

-3

1

-3

-3

1

-3

-3

3

1

-3

-1

-3

-3

-3

-1

1

1

3

9

3

-1

3

1

-3

-3

-1

1

-3

-3

3

3

3

1

3

-3

3

-3

10

-3

-3

-3

1

-3

3

1

1

3

-3

-3

1

3

-1

3

-3

-3

3

11

-3

-3

3

3

3

-1

-1

-3

-1

-1

-1

3

1

-3

-3

-1

3

-1

12

-3

-1

-3

-3

1

1

-1

-3

-1

-3

-1

-1

3

3

-1

3

1

3

13

1

1

-3

-3

-3

-3

1

3

-3

3

3

1

-3

-1

3

-1

-3

1

14

-3

3

-1

-3

-1

-3

1

1

-3

-3

-1

-1

3

-3

1

3

1

1

15

3

1

-3

1

-3

3

3

-1

-3

-3

-1

-3

-3

3

-3

-1

1

3

16

-3

-1

-3

-1

-3

1

3

-3

-1

3

3

3

1

-1

-3

3

-1

-3

17

-3

-1

3

3

-1

3

-1

-3

-1

1

-1

-3

-1

-1

-1

3

3

1

18

-3

1

-3

-1

-1

3

1

-3

-3

-3

-1

-3

-3

1

1

1

-1

-1

19

3

3

3

-3

-1

-3

-1

3

-1

1

-1

-3

1

-3

-3

-1

3

3

20

-3

1

1

-3

1

1

3

-3

-1

-3

-1

3

-3

3

-1

-1

-1

-3

21

1

-3

-1

-3

3

3

-1

-3

1

-3

-3

-1

-3

-1

1

3

3

3

22

-3

-3

1

-1

-1

1

1

-3

-1

3

3

3

3

-1

3

1

3

1

23

3

-1

-3

1

-3

-3

-3

3

3

-1

1

-3

-1

3

1

1

3

3

24

3

-1

-1

1

-3

-1

-3

-1

-3

-3

-1

-3

1

1

1

-3

-3

3

25

-3

-3

1

-3

3

3

3

-1

3

1

1

-3

-3

-3

3

-3

-1

-1

26

-3

-1

-1

-3

1

-3

3

-1

-1

-3

3

3

-3

-1

3

-1

-1

-1

27

-3

-3

3

3

-3

1

3

-1

-3

1

-1

-3

3

-3

-1

-1

-1

3

28

-1

-3

1

-3

-3

-3

1

1

3

3

-3

3

3

-3

-1

3

-3

1

29

-3

3

1

-1

-1

-1

-1

1

-1

3

3

-3

-1

1

3

-1

3

-1

 

Table 5.2.2.2-4: Definition of \(\varphi(n)\) for \(M_{zC}=24\)

\[\mathbf{u}\]

\[\mathbf{\varphi}(0),\ldots,\mathbf{\varphi}(23)\]

0

-1

-3

3

-1

3

1

3

-1

1

-3

-1

-3

-1

1

3

-3

-1

-3

3

3

3

-3

-3

-3

1

-1

-3

3

1

1

-3

1

-3

-3

1

-3

-1

-1

3

-3

3

3

3

-3

1

3

3

-3

-3

2

-1

-3

-3

1

-1

-1

-3

1

3

-1

-3

-1

-1

-3

1

1

3

1

-3

-1

-1

3

-3

-3

3

1

-3

3

-1

-3

-1

3

3

1

-1

1

1

3

-3

-1

-3

-3

-3

-1

3

-3

-1

-3

-3

4

-1

3

-3

-3

-1

3

-1

-1

1

3

1

3

-1

-1

-3

1

3

1

-1

-3

1

-1

-3

-3

5

-3

-1

1

-3

-3

1

1

-3

3

-1

-1

-3

1

3

1

-1

-3

-1

-3

1

-3

-3

-3

-3

6

-3

3

1

3

-1

1

-3

1

-3

1

-1

-3

-1

-3

-3

-3

-3

-1

-1

-1

1

1

-3

-3

7

-3

1

3

-1

1

-1

3

-3

3

-1

-3

-1

-3

3

-1

-1

-1

-3

-1

-1

-3

3

3

-3

8

-3

1

-3

3

-1

-1

-1

-3

3

1

-1

-3

-1

1

3

-1

1

-1

1

-3

-3

-3

-3

-3

9

1

1

-1

-3

-1

1

1

-3

1

-1

1

-3

3

-3

-3

3

-1

-3

1

3

-3

1

-3

-3

10

-3

-3

-3

-1

3

-3

3

1

3

1

-3

-1

-1

-3

1

1

3

1

-1

-3

3

1

3

-3

11

-3

3

-1

3

1

-1

-1

-1

3

3

1

1

1

3

3

1

-3

-3

-1

1

-3

1

3

-3

12

3

-3

3

-1

-3

1

3

1

-1

-1

-3

-1

3

-3

3

-1

-1

3

3

-3

-3

3

-3

-3

13

-3

3

-1

3

-1

3

3

1

1

-3

1

3

-3

3

-3

-3

-1

1

3

-3

-1

-1

-3

-3

14

-3

1

-3

-1

-1

3

1

3

-3

1

-1

3

3

-1

-3

3

-3

-1

-1

-3

-3

-3

3

-3

15

-3

-1

-1

-3

1

-3

-3

-1

-1

3

-1

1

-1

3

1

-3

-1

3

1

1

-1

-1

-3

-3

16

-3

-3

1

-1

3

3

-3

-1

1

-1

-1

1

1

-1

-1

3

-3

1

-3

1

-1

-1

-1

-3

17

3

-1

3

-1

1

-3

1

1

-3

-3

3

-3

-1

-1

-1

-1

-1

-3

-3

-1

1

1

-3

-3

18

-3

1

-3

1

-3

-3

1

-3

1

-3

-3

-3

-3

-3

1

-3

-3

1

1

-3

1

1

-3

-3

19

-3

-3

3

3

1

-1

-1

-1

1

-3

-1

1

-1

3

-3

-1

-3

-1

-1

1

-3

3

-1

-3

20

-3

-3

-1

-1

-1

-3

1

-1

-3

-1

3

-3

1

-3

3

-3

3

3

1

-1

-1

1

-3

-3

21

3

-1

1

-1

3

-3

1

1

3

-1

-3

3

1

-3

3

-1

-1

-1

-1

1

-3

-3

-3

-3

22

-3

1

-3

3

-3

1

-3

3

1

-1

-3

-1

-3

-3

-3

-3

1

3

-1

1

3

3

3

-3

23

-3

-1

1

-3

-1

-1

1

1

1

3

3

-1

1

-1

1

-1

-1

-3

-3

-3

3

1

-1

-3

24

-3

3

-1

-3

-1

-1

-1

3

-1

-1

3

-3

-1

3

-3

3

-3

-1

3

1

1

-1

-3

-3

25

-3

1

-1

-3

-3

-1

1

-3

-1

-3

1

1

-1

1

1

3

3

3

-1

1

-1

1

-1

-3

26

-1

3

-1

-1

3

3

-1

-1

-1

3

-1

-3

1

3

1

1

-3

-3

-3

-1

-3

-1

-3

-3

27

3

-3

-3

-1

3

3

-3

-1

3

1

1

1

3

-1

3

-3

-1

3

-1

3

1

-1

-3

-3

28

-3

1

-3

1

-3

1

1

3

1

-3

-3

-1

1

3

-1

-3

3

1

-1

-3

-3

-3

-3

-3

29

3

-3

-1

1

3

-1

-1

-3

-1

3

-1

-3

-1

-3

3

-1

3

1

1

-3

3

-3

-3

-3

 

5.2.3     Low-PAPR sequence generation type 2 #

The low-PAPR sequence \(r_{u,v}^{(\alpha,\delta)}(n)\) is defined by a base sequence \({\bar{r}}_{u,v}(n)\) according to

\[r_{u,v}^{(\alpha,\delta)}(n) = {\bar{r}}_{u,v}(n),0 \leq n < M\]

where \(M = {{mN_{\text{sc}}^{\text{RB}}}/2^{\delta}}\) is the length of the sequence.

Base sequences \({\bar{r}}_{u,v}(n)\) are divided into groups, where \(u \in \left\{ {0,1,\ldots,29} \right\}\) is the group number and \(v\) is the base sequence number within the group, such that each group contains one base sequence (\(v = 0\)) of length \(M = {{mN_{\text{sc}}^{\text{RB}}}/2^{\delta}}\), \(1/{2 \leq {m/2^{\delta}}}\). The sequence \({\bar{r}}_{u,v}(0),\ldots,{\bar{r}}_{u,v}\left( {M - 1} \right)\) is defined by

\[\begin{matrix} {{\bar{r}}_{u,v}(n) = \frac{1}{\sqrt[{}]{M}}\sum\limits_{i = 0}^{M - 1}{{\overset{\sim}{r}}_{u,v}(i)e^{- j\frac{2\pi in}{M}}}} \\ {n = 0,\ldots,M - 1} \end{matrix}\]

where the definition of \({\overset{\sim}{r}}_{u,v}(i)\) depends on the sequence length.

5.2.3.1     Sequences of length 30 or larger #

For \(M \geq 30\), the sequence \({\overset{\sim}{r}}_{u,v}(i)\) is obtained as the complex-valued modulations symbols resulting from π/2-BPSK modulation as defined in clause 5.1.1 applied to the binary sequence \(c(i)\) given by clause 5.2.1, initialized with \(c_{\text{init}}\).

5.2.3.2     Sequences of length less than 30 #

For \(M = 6\), the sequence \({\overset{\sim}{r}}_{u,v}(i)\) is given by

\[{\overset{\sim}{r}}_{u,v}(i) = e^{j{{\varphi{(i)}\pi}/8}},0 \leq i \leq M - 1\]

where the value of \(\varphi(i)\) is given by Table 5.2.3.2-1.

For \(M \in \left\{ {12,18,24} \right\}\), the sequence \({\overset{\sim}{r}}_{u,v}(i)\) is obtained as the complex-valued modulations symbols resulting from π/2-BPSK modulation as defined in clause 5.1.1 applied to the binary sequence \(b(i)\) given by Tables 5.2.3.2-2 to 5.2.3.2-4.

 

Table 5.2.3.2-1: Definition of \(\mathbf{\varphi}\left( \mathbf{i} \right)\) for \(\mathbf{M} = 6\).

\[\mathbf{u}\]

\[\mathbf{\varphi}(0),\ldots,\mathbf{\varphi}(5)\]

0

-1

-7

-3

-5

-1

3

1

-1

3

7

-3

7

3

2

-1

3

1

5

-1

-5

3

-7

-3

-7

5

-7

-3

4

7

5

-1

-7

-3

1

5

3

-3

1

5

-1

-1

6

-7

-3

-7

-3

7

-5

7

-7

-3

1

-5

-1

-5

8

-7

-3

3

-3

-7

-3

9

-7

-7

-1

1

-5

1

10

-7

-3

-7

5

-1

5

11

-7

-7

-3

1

5

-1

12

5

7

-3

-5

5

-5

13

-3

7

-5

-1

-5

-1

14

5

-7

7

1

5

1

15

-7

3

1

5

-1

3

16

-7

-5

-1

-7

-5

5

17

-7

1

-3

3

7

5

18

-7

-7

3

5

1

5

19

-7

-3

3

-1

3

-5

20

-7

-5

5

3

-7

-1

21

1

5

1

5

3

7

22

1

-3

1

-5

-1

3

23

1

7

1

-5

-7

-1

24

1

-1

3

-1

-7

-3

25

1

-1

-5

-1

3

-3

26

1

-1

3

-1

3

7

27

-5

3

7

5

3

7

28

-7

1

-3

1

5

1

29

1

5

3

-7

5

-3

 

Table 5.2.3.2-2: Definition of \(\mathbf{b}\left( \mathbf{i} \right)\) for \(\mathbf{M} = 12\).

\[\mathbf{u}\]

\[\mathbf{b}(0),\ldots,\mathbf{b}(11)\]

0

0

0

0

0

0

0

1

1

0

1

1

0

1

0

0

0

0

0

1

0

0

0

1

1

1

2

0

0

0

0

0

1

1

1

0

1

1

1

3

1

1

0

1

1

0

1

0

1

0

0

0

4

1

1

0

0

1

0

1

0

1

0

0

1

5

1

0

1

1

0

1

0

0

1

0

1

1

6

0

0

0

1

0

0

1

0

0

0

1

0

7

0

1

0

0

0

1

0

0

1

0

0

0

8

1

0

1

1

1

1

0

1

1

0

1

1

9

1

0

1

1

0

1

1

1

1

0

0

0

10

1

0

1

1

0

1

0

0

0

1

1

0

11

1

0

1

0

0

1

0

0

1

0

1

0

12

1

1

0

0

0

0

0

1

1

1

1

0

13

0

1

0

0

0

1

1

0

1

0

1

1

14

0

0

0

0

0

1

1

0

0

0

1

1

15

0

0

0

0

0

1

0

0

1

0

0

1

16

0

0

1

0

0

1

0

0

0

0

0

1

17

0

0

0

0

0

1

1

0

1

1

1

0

18

0

0

0

1

1

1

1

1

0

0

0

1

19

1

0

0

0

1

0

0

0

0

0

1

1

20

0

1

1

1

1

0

1

0

1

1

1

1

21

0

1

1

1

0

1

0

0

1

1

0

1

22

0

1

1

1

1

1

0

0

1

0

0

0

23

0

1

1

1

0

0

0

0

0

1

0

0

24

0

0

1

1

1

1

1

1

1

1

0

0

25

0

1

1

1

0

0

1

1

0

1

0

0

26

0

1

1

1

0

1

1

1

0

1

1

1

27

0

1

1

1

1

1

1

0

0

0

1

1

28

0

1

1

1

1

0

0

0

0

0

1

1

29

0

1

1

1

0

1

1

1

1

0

1

1

 

Table 5.2.3.2-3: Definition of \(\mathbf{b}\left( \mathbf{i} \right)\) for \(\mathbf{M} = 18\).

\[\mathbf{u}\]

\[\mathbf{b}(0),\ldots,\mathbf{b}(17)\]

0

0

0

0

0

0

1

0

0

0

1

1

1

1

1

0

0

0

1

1

0

0

0

0

0

0

0

1

1

1

1

1

0

0

1

0

0

1

2

0

0

0

0

0

1

1

1

1

0

1

1

1

0

1

1

1

1

3

0

1

0

1

1

0

1

1

0

0

0

1

1

0

1

0

1

1

4

1

1

0

1

0

0

1

0

1

0

1

0

0

1

1

1

1

0

5

0

1

0

1

0

1

1

1

0

0

1

0

1

1

0

1

1

0

6

0

0

0

1

1

1

0

0

0

1

0

0

0

1

1

1

1

1

7

0

1

0

1

0

0

0

1

1

0

1

0

0

0

0

0

1

1

8

0

0

1

0

1

0

0

0

1

0

1

0

0

1

0

0

0

1

9

1

0

1

1

0

0

1

0

1

0

1

0

0

1

0

0

0

1

10

1

0

1

1

0

0

0

1

1

1

0

0

0

0

0

0

0

1

11

1

1

0

1

1

0

1

1

1

0

1

1

1

1

1

0

0

0

12

1

0

0

0

1

0

1

0

1

0

0

0

1

1

0

1

0

1

13

1

0

1

1

0

1

0

1

1

1

0

0

0

0

0

1

1

0

14

0

0

0

0

0

1

1

1

0

1

1

0

1

0

1

1

0

0

15

0

0

1

1

1

0

1

1

0

1

0

0

0

1

1

0

1

0

16

0

1

0

0

1

0

0

0

1

1

1

0

1

0

0

1

1

1

17

0

1

0

0

1

1

0

1

1

0

0

0

0

0

0

0

1

0

18

0

0

1

0

0

1

1

1

1

0

0

0

0

0

1

1

0

0

19

0

0

0

0

0

0

0

1

0

0

1

0

0

1

1

0

1

1

20

0

0

0

0

0

1

1

0

0

0

0

1

0

0

1

1

1

1

21

1

1

1

1

0

1

0

1

1

1

1

1

0

0

1

0

0

1

22

1

0

0

1

0

0

0

1

0

0

1

1

1

1

0

1

1

1

23

0

0

1

0

0

0

1

1

1

0

0

0

1

0

0

1

0

1

24

1

1

0

1

1

0

0

0

0

0

0

0

1

1

0

1

1

0

25

1

1

0

1

0

1

0

1

1

0

0

0

0

1

0

0

1

0

26

0

1

1

1

1

1

1

1

0

0

1

0

1

0

0

1

0

0

27

0

1

1

0

1

1

1

0

0

0

0

0

0

0

1

1

0

0

28

0

0

0

1

1

0

0

0

0

0

0

0

0

0

1

1

0

0

29

0

1

1

1

0

1

1

0

1

0

1

1

1

0

1

1

0

0

 

Table 5.2.3.2-4: Definition of \(\mathbf{b}\left( \mathbf{i} \right)\) for \(\mathbf{M} = 24\)

\[\mathbf{u}\]

\[\mathbf{b}(0),\ldots,\mathbf{b}(23)\]

0

0

0

0

0

0

0

0

1

0

0

1

1

1

1

1

0

0

1

0

0

1

0

0

1

1

0

0

0

0

0

0

0

1

0

0

1

0

1

1

0

1

1

1

0

0

0

1

1

0

2

0

0

0

0

0

0

0

0

1

0

0

1

0

0

1

0

0

1

1

1

1

0

1

1

3

0

0

0

0

0

0

0

0

1

1

0

1

1

0

0

1

0

1

0

1

1

0

1

1

4

1

0

0

1

1

1

1

1

0

1

1

0

1

1

1

0

1

1

0

0

0

1

1

1

5

1

0

1

0

1

1

0

1

1

0

0

1

1

1

1

1

0

0

1

1

0

1

1

1

6

0

1

1

0

0

1

0

0

1

1

1

1

1

1

0

1

1

1

1

0

1

1

0

1

7

1

0

1

1

1

1

1

1

1

1

1

0

1

0

0

1

1

1

0

0

1

1

0

1

8

0

0

1

0

0

1

0

1

0

0

0

1

0

0

1

0

0

0

0

0

1

1

1

0

9

0

0

0

0

1

0

0

1

1

0

1

0

0

0

0

0

1

1

0

0

0

1

0

1

10

1

0

1

0

0

0

1

1

1

0

0

1

1

1

1

0

1

1

1

1

0

0

1

0

11

0

0

1

0

0

1

0

0

0

0

0

1

1

1

0

0

0

1

0

0

1

0

1

0

12

1

0

1

0

0

1

1

1

0

1

0

0

0

1

0

1

1

1

0

0

1

0

1

1

13

1

0

1

0

0

1

1

0

1

1

0

1

0

1

0

1

1

0

1

1

0

0

1

0

14

1

0

1

0

0

0

1

0

0

1

1

1

0

0

0

0

0

1

0

0

1

0

1

1

15

1

0

0

1

0

1

0

0

1

1

0

0

0

0

1

1

1

1

1

1

1

0

0

1

16

0

0

0

1

1

1

1

0

0

1

0

1

0

0

1

1

1

0

1

1

1

0

0

1

17

1

1

0

1

0

1

1

1

0

0

1

1

1

0

0

0

0

0

0

1

1

0

1

0

18

0

0

0

0

0

0

0

0

0

1

1

1

1

0

0

0

1

0

1

1

0

0

0

1

19

1

0

0

0

1

0

1

1

0

0

0

1

0

0

0

0

0

0

0

0

0

1

1

1

20

0

0

0

0

0

0

1

1

1

0

1

1

0

0

0

1

1

0

0

0

1

0

1

0

21

0

1

1

0

1

0

1

1

1

0

0

0

0

1

0

0

0

0

1

0

0

0

1

1

22

1

0

1

0

0

1

0

0

0

0

0

1

1

1

0

0

1

0

0

0

1

0

1

1

23

1

0

0

1

1

0

1

0

0

0

0

0

1

1

1

1

1

1

1

1

0

0

1

1

24

1

0

0

0

1

1

0

1

0

1

0

0

1

0

0

1

1

1

1

1

1

0

0

0

25

1

0

1

0

1

1

0

0

0

1

0

0

0

1

1

1

1

1

1

0

0

1

0

0

26

0

1

0

0

1

0

1

0

1

1

0

0

0

1

1

1

1

1

1

0

0

1

0

0

27

0

1

0

1

1

0

1

0

1

0

1

0

1

1

0

1

1

0

0

1

0

0

1

1

28

0

1

0

0

0

1

1

0

1

0

1

0

1

1

1

0

1

0

0

1

0

0

1

1

29

0

1

0

0

1

0

0

1

1

1

1

1

1

1

1

1

1

0

0

1

0

0

1

1

 

5.3     OFDM baseband signal generation #

5.3.1     OFDM baseband signal generation for all channels except PRACH and RIM-RS #

The time-continuous signal \(s_{l}^{(p,\mu)}(t)\) on antenna port \(p\) and subcarrier spacing configuration \(\mu\) for OFDM symbol \(l \in \{0,1,\ldots, N_{\text{slot}}^{\text{subframe},\mu} N_{\text{symb}}^{\text{slot}} - 1\}\) in a subframe for any physical channel or signal except PRACH is defined by

\[\begin{matrix} {{\bar{s}}_{l}^{(p,\mu)}(t) = \sum\limits_{k = 0}^{N_{\text{grid,}x}^{\text{size},\mu}N_{\text{sc}}^{\text{RB}} - 1}{a_{k,l}^{(p,\mu)}e^{j2\pi{({k + k_{0}^{\mu} - {{N_{\text{grid,}x}^{\text{size},\mu}N_{\text{sc}}^{\text{RB}}}/2}})}\Delta f{({t - N_{\text{CP},l}^{\mu}T_{\text{c}} - t_{\text{start,}l}^{\mu}})}}}} \\ {k_{0}^{\mu} = \left( {N_{\text{grid,}x}^{\text{start},\mu} + {N_{\text{grid,}x}^{\text{size},\mu}/2}} \right)N_{\text{sc}}^{\text{RB}} - \left( {N_{\text{grid,}x}^{\text{start},\mu_{0}} + {N_{\text{grid,}x}^{\text{size},\mu_{0}}/2}} \right)N_{\text{sc}}^{\text{RB}}2^{\mu_{0} - \mu}} \\ {T_{\text{symb,}l}^{\mu} = \left( {N_{\text{u}}^{\mu} + N_{\text{CP},l}^{\mu}} \right)T_{\text{c}}} \end{matrix}\]

where \(t = 0\) at the start of the subframe,

\(\begin{aligned} N_u^{\mu} &= 2048\,\kappa\cdot 2^{-\mu},\\ N_{CP,l}^{\mu} &= \begin{cases} 512\,\kappa\cdot 2^{-\mu}, & \text{extended cyclic prefix},\\ 144\,\kappa\cdot 2^{-\mu} + 16\,\kappa, & \text{normal cyclic prefix, } l=0 \text{ or } l=7\cdot 2^{\mu},\\ 144\,\kappa\cdot 2^{-\mu}, & \text{normal cyclic prefix, } l\neq 0 \text{ and } l\neq 7\cdot 2^{\mu}. \end{cases} \end{aligned}\)

and

-    \(\Delta f\) is given by clause 4.2;

-    \(\mu\) is the subcarrier spacing configuration;

-    \(\mu_{0}\) is the largest \(\mu\) value among the subcarrier spacing configurations by scs-SpecificCarrierList for each of uplink and downlink and by sl-SCS-SpecificCarrierList for sidelink.

The starting position of OFDM symbol \(l\) for subcarrier spacing configuration \(\mu\) in a subframe is given by

    \(t_{start,l}^{\mu} = \begin{cases} 0 & {l = 0} \\ {t_{start,l - 1}^{\mu} + T_{symb,l - 1}^{\mu}} & \text{otherwise} \end{cases}\)

In case of cyclic prefix extension of the first OFDM symbol \(l\) allocated for PUSCH, SRS, PUCCH, PSCCH/PSSCH, PSFCH, or S-SS/PSBCH block transmission, the time-continuous signal \(s_{\text{ext}}^{(p,\mu)}(t)\) for the interval \({t_{\text{start,}l}^{\mu} - T}_{\text{ext}} \leq t < t_{\text{start,}l}^{\mu}\) preceding the first OFDM symbol for PUSCH, SRS, PUCCH, PSCCH/PSSCH, PSFCH, or S-SS/PSBCH block is given by

\[s_{\text{ext}}^{(p,\mu)}(t) = {\bar{s}}_{l}^{(p,\mu)}(t)\]

where \(t < 0\) refers to the signal in the previous subframe and

-    for dynamically scheduled PUSCH, SRS, and PUCCH transmissions

\[T_{\text{ext}}\text{=min}\left( {\max\left( {T_{\text{ext}}^{'},0} \right),T_{\text{symb},(l - 1)\text{mod7∙}2^{\mu}}^{\mu}} \right)\]

\[T_{\text{ext}}^{'} = \sum_{k = 1}^{C_{i}}T_{symb,{({l - k})}mod7 \bullet 2^{\mu}}^{\mu} - \Delta_{i}\]

    where \(\Delta_{i}\) is given by Table 5.3.1-1 with \(C_{1} = 1\) for \(\mu \in \left\{ 0,1 \right\}\), \(C_{1} = 2\) for \(\mu = 2\), and \(C_{2}\) and \(C_{3}\) given by the higher-layer parameters cp-ExtensionC2 and cp-ExtensionC3, respectively, and \(T_{\text{TA}}\) given by clause 4.3.1. For contention-based random access, or in absence of higher-layer configuration of \(C_{2}\) and \(C_{3}\), the value of \(C_{i}\)shall be set to the largest integer fulfilling \(T_{\text{ext}}^{'} < T_{symb,(l - 1)\text{mod7∙}2^{\mu}}^{\mu}\) for each of the values of \(i \in \left\{ 2,3 \right\}\). Text is applied to the first UL transmission scheduled by the scheduling DCI.

-    for a PUSCH transmission using configured grant

\[T_{\text{ext}} = \sum_{k = 1}^{2^{\mu}}T_{symb,{({l - k})}mod7 \bullet 2^{\mu}}^{\mu} - \Delta_{i}\]

    where \(\Delta_{i}\) is given by Table 5.3.1-2 with the index \(i\) given by the procedure in [6, TS 38.214].

-    for PSCCH/PSSCH, PSFCH, and S-SS/PSBCH block transmission

\[T_{\text{ext}} = \max\left( {\sum_{k = 1}^{C_{i}}T_{symb,{({l - k})}mod7 \bullet 2^{\mu}}^{\mu} - \Delta_{i},0} \right)\]

    where \(\Delta_{i}\) and \(C_{i}\) are given by Table 5.3.1-3 with the index \(i\) given by the procedure in [5, TS 38.213] or [6, TS 38.214].

 

Table 5.3.1-1: The variables \(\mathbf{C}_{\mathbf{i}}\) and \(\mathbf{\Delta}_{\mathbf{i}}\) for uplink cyclic prefix extension

\(\mathbf{T}_{\text{ext}}\)index \(\mathbf{i}\)

\[\mathbf{C}_{\mathbf{i}}\]

\[\mathbf{\Delta}_{\mathbf{i}}\]

0

-

-

1

\[C_{1}\]

\[25 \bullet 10^{- 6}\]

2

\[C_{2}\]

\[16 \bullet 10^{- 6} + T_{\text{TA}}\]

3

\[C_{3}\]

\[25 \bullet 10^{- 6} + T_{\text{TA}}\]

 

Table 5.3.1-2: The variable \(\mathbf{\Delta}_{\mathbf{i}}\) for uplink cyclic prefix extension with configured grants.

index \(\mathbf{i}\)

\[\mathbf{\Delta}_{\mathbf{i}}\]

0

\[16 \bullet 10^{- 6}\]

1

\[25 \bullet 10^{- 6}\]

2

\[34 \bullet 10^{- 6}\]

3

\[43 \bullet 10^{- 6}\]

4

\[52 \bullet 10^{- 6}\]

5

\[61 \bullet 10^{- 6}\]

6

\[\sum_{k = 1}^{2^{\mu}}T_{symb,{({l - k})}mod7 \bullet 2^{\mu}}^{\mu}\]

 

Table 5.3.1-3: The variables \(\mathbf{C}_{\mathbf{i}}\) and \(\mathbf{\Delta}_{\mathbf{i}}\) for sidelink cyclic prefix extension

Index \(\mathbf{i}\)

\[\mathbf{\mu} = 0\]

\[\mathbf{\mu} = 1\]

\[\mathbf{\mu} = 2\]

\[\mathbf{C}_{\mathbf{i}}\]

\[\mathbf{\Delta}_{\mathbf{i}}\]

\[\mathbf{C}_{\mathbf{i}}\]

\[\mathbf{\Delta}_{\mathbf{i}}\]

\[\mathbf{C}_{\mathbf{i}}\]

\[\mathbf{\Delta}_{\mathbf{i}}\]

0

-

-

-

-

-

-

1

1

\[16 \bullet 10^{- 6}\]

1

\[16 \bullet 10^{- 6}\]

1

\[16 \bullet 10^{- 6}\]

2

1

\[25 \bullet 10^{- 6}\]

1

\[25 \bullet 10^{- 6}\]

2

\[16 \bullet 10^{- 6}\]

3

1

\[34 \bullet 10^{- 6}\]

2

\[16 \bullet 10^{- 6}\]

2

\[25 \bullet 10^{- 6}\]

4

1

\[43 \bullet 10^{- 6}\]

2

\[25 \bullet 10^{- 6}\]

reserved

reserved

5

1

\[52 \bullet 10^{- 6}\]

2

\[34 \bullet 10^{- 6}\]

reserved

reserved

6

1

\[61 \bullet 10^{- 6}\]

2

\[43 \bullet 10^{- 6}\]

reserved

reserved

7

reserved

reserved

2

\[52 \bullet 10^{- 6}\]

reserved

reserved

8

reserved

reserved

2

\[61 \bullet 10^{- 6}\]

reserved

reserved

 

5.3.2     OFDM baseband signal generation for PRACH #

The time-continuous signal \(s_{l}^{(p,\mu)}(t)\) on antenna port \(p\) for PRACH is defined by

sl(p,μ)t=k=0LRA-1ak(p,RA)ej2πk+Kk1+kΔfRAt-NCP,lRATc-tstartRAK=Δf/ΔfRAk1=k0μ+NBWP,istart-Ngridstart,μNscRB-Ngridsize,μNscRB/2+nRAstartNscRB+nRANRBRANscRBif LRA139, 839nRANRBRANscRBif LRA571, 1151 in FR2-2NRB,UL,n0+nRAstart,μ-NRB,UL,n0start,μNscRBif LRA571, 1151 in FR1k0μ=Ngridstart,μ+Ngridsize,μ/2NscRB-Ngridstart,μ0+Ngridsize,μ0/2NscRB2μ0-μ

where \(t_{\text{start}}^{\mathrm{RA}} \le t < t_{\text{start}}^{\mathrm{RA}} + \left(N_u + N_{\mathrm{CP},l}^{\mathrm{RA}}\right) T_c\) and

-    \(\bar{k}\) is given by clause 6.3.3;

-    \(\Delta f\) is the subcarrier spacing of the initial uplink bandwidth part during initial access. If the PRACH transmission is for a candidate cell \(\Delta f\) is provided by ltm-PRACH-SubcarrierSpacing in EarlyUL-SyncConfig. Otherwise, \(\Delta f\) is the subcarrier spacing of the active uplink bandwidth part;

-    \(\mu_{0}\) is the largest \(\mu\) value among the subcarrier spacing configurations by the higher-layer parameter scs-SpecificCarrierList;

-    \(N_{BWP,i}^{\text{start}}\) is the lowest numbered resource block of the initial uplink bandwidth part and is derived by the higher-layer parameter initialUplinkBWP or initialUplinkBWP-RedCap during initial access and from the higher-layer parameters bwp-GenericParameters in EarlyUL-SyncConfig if the PRACH transmission is for a candidate cell. Otherwise, \(N_{BWP,i}^{\text{start}}\) is the lowest numbered resource block of the active uplink bandwidth part and is derived by the higher-layer parameter BWP-Uplink;

-    \(n_{\text{RA}}^{\text{start}}\) is the frequency offset of the lowest PRACH transmission occasion in frequency domain and is given by the higher-layer parameter msgA-RO-FrequencyStart if configured and a type-2 random-access procedure is initiated as described in clause 8.1 of [5, TS 38.213], otherwise by msg1-FrequencyStart as described in clause 8.1 of [5 TS 38.213]:

-    if the higher-layer parameter sbfd-RACHSingleConfig is configured, the quantity \(n_{\text{RA}}^{\text{start}}\) is defined relative the lowest-numbered physical resource block from the physical resource blocks that are both in the active uplink bandwidth part and in the uplink sub-band;

-    otherwise, the quantity \(n_{\text{RA}}^{\text{start}}\) is defined relative to physical resource block 0 of the active uplink bandwidth part.

-    \(n_{\mathrm{RA}}\) is the PRACH transmission occasion index in frequency domain for a given PRACH transmission occasion in one time instance as given by clause 6.3.3.2;

-    \(N^{RA}_{RB}\) is the number of resource blocks occupied and is given by the parameter allocation expressed in number of RBs for PUSCH in Table 6.3.3.2-1.

-    \(N_{\text{RB,UL},n}^{\text{start},\mu}\) is the start CRB index of uplink RB set \(n\) corresponding to the quantity \({RB}_{n,\text{UL}}^{start,\mu}\). The UE assumes that the RB set is defined as when the UE is not provided IntraCellGuardBandsPerSCS for an UL carrier as described in Clause 7 of [6, TS 38.214]

-    \(n_{0}\) is the index of the RB set which contains the lowest PRACH transmission occasion in frequency domain indicated by \(n_{\text{RA}}^{\text{start}}\). The UE may assume that \(n_{\text{RA}}^{\text{start}}\) is configured such that each PRACH transmission occasion is fully contained within an RB set.

-    \(L_{RA}\) and \(N_{u}\) are given by clause 6.3.3

-    \(N_{\text{CP},l}^{\text{RA}} = N_{\text{CP}}^{\text{RA}} + n \bullet 16\kappa\) where

-    for \(\Delta f_{\mathrm{RA}} \in \{1.25, 5\}\,\mathrm{kHz}\), \(n = 0\)

-    for \(\Delta f_{\text{RA}} \in \left\{ 15,30,60,120,480,960 \right\}\)kHz, \(n\) is the number of times the interval \(\left\lbrack {t_{\text{start}}^{\text{RA}},\left. {t_{\text{start}}^{\text{RA}} + \left( {N_{\text{u}}^{\text{RA}} + N_{\text{CP}}^{\text{RA}}} \right)T_{\text{c}}} \right)} \right.\) overlaps with either time instance 0 or time instance \(\left(\Delta f_{\max}\,\frac{N_f}{2000}\right)\cdot T_c = 0.5\,\mathrm{ms}\) in a subframe

The starting position \(t_{\text{start}}^{\text{RA}}\) of the PRACH preamble in a subframe (for \(\Delta f_{\mathrm{RA}} \in \{1.25, 5, 15, 30\}\,\mathrm{kHz}\)) or in a 60 kHz slot (for \(\Delta f_{\text{RA}} \in \left\{ 60,120,480,960 \right\}\)kHz) is given by

    \(t^{\mathrm{RA}}_{\mathrm{start}} = t^{\mu}_{\mathrm{start},l} t^{\mu}_{\mathrm{start},l} = \begin{cases} 0, & l=0,\\ t^{\mu}_{\mathrm{start},l-1} + \left(N^{\mu}_{u} + N^{\mu}_{\mathrm{CP},l-1}\right) T_c, & \text{otherwise} \end{cases}\)

where

-    the subframe or 60 kHz slot is assumed to start at \(t = 0\);

-    a timing advance value \(N_{\text{TA}} = 0\) shall be assumed;

-    \(N_{\text{u}}^{\mu}\) and \(N_{\text{CP,}l - 1}^{\mu}\) are given by clause 5.3.1;

-    \(\mu = 0\) shall be assumed for \(\mathrm{\Delta}f_{\text{RA}} \in \left\{ {1.25,5} \right\}\) kHz, otherwise the value of \(\mu\) corresponds to \(\mathrm{\Delta}f_{\text{RA}} \in \left\{ {15,30,60,120,480,960} \right\}\) kHz and the symbol position \(l\) is given by

    \(l = l_{0} + n_{t}^{\text{RA}}N_{\text{dur}}^{\text{RA}} + 14n_{\text{slot}}^{\text{RA}}\)

where

-    \(\ell_0\) is given by the parameter "starting symbol" in Tables 6.3.3.2-2 to 6.3.3.2-4;

-    \(n_t^{RA}\) is the PRACH transmission occasion within the PRACH slot, numbered in increasing order from 0 to \(N_{t}^{\text{RA,slot}} - 1\) within a RACH slot where \(N_{t}^{\mathrm{RA,slot}}\) is given Tables 6.3.3.2-2 to 6.3.3.2-4 for \(L_{\text{RA}} \in \left\{ 139,571,1151 \right\}\) and fixed to 1 for \(L_{RA} = 839\);

-    \(N^{\mathrm{RA}}_{\mathrm{dur}}\) is given by Tables 6.3.3.2-2 to 6.3.3.2-4;

-    \(n_{\mathrm{slot}}^{\mathrm{RA}}\) is given by

-    if \(\mathrm{\Delta}f_{\text{RA}} \in \left\{ {1.25,5,15,60} \right\}\) kHz, then \(n_{\mathrm{slot}}^{\mathrm{RA}}=0\)

-    if \(\mathrm{\Delta}f_{\text{RA}} \in \left\{ {30,120} \right\}\) kHz and either of "Number of PRACH slots within a subframe" in Tables 6.3.3.2-2 to 6.3.3.2-3 or "Number of PRACH slots within a 60 kHz slot" in Table 6.3.3.2-4 is equal to 1, then \(n_{\text{slot}}^{\text{RA}} = 1\), otherwise \(n_{\text{slot}}^{\text{RA}} \in \left\{ 0,1 \right\}\)

-    if \(\mathrm{\Delta}f_{\text{RA}} \in \left\{ {480,960} \right\}\) kHz and

-    the "Number of PRACH slots within a 60 kHz slot" in Table 6.3.3.2-4 is equal to 1, then \(n_{\text{slot}}^{\text{RA}} = 7\) for \(\mathrm{\Delta}f_{\text{RA}} = 480\) kHz and \(n_{\text{slot}}^{\text{RA}} = 15\) for \(\mathrm{\Delta}f_{\text{RA}} = 960\)kHz, or

-    the "Number of PRACH slots within a 60 kHz slot" in Table 6.3.3.2-4 is equal to 2, then \(n_{\text{slot}}^{\text{RA}} \in \left\{ 3,7 \right\}\) for \(\mathrm{\Delta}f_{\text{RA}} = 480\)kHz and \(n_{\text{slot}}^{\text{RA}} \in \left\{ 7,15 \right\}\) for \(\mathrm{\Delta}f_{\text{RA}} = 960\)kHz.

If the preamble format given by Tables 6.3.3.2-2 to 6.3.3.2-4 is A1/B1, A2/B2 or A3/B3, then

-    if \(n_{t}^{\text{RA}} = N_{t}^{\text{RA,slot}} - 1\), then the PRACH preamble with the corresponding PRACH preamble format from B1, B2 and B3 is transmitted in the PRACH transmission occasion;

-    otherwise the PRACH preamble with the corresponding PRACH preamble format from A1, A2 and A3 is transmitted in the PRACH transmission occasion

5.3.3     OFDM baseband signal generation for RIM-RS #

The time-continuous signal \(s_{l}^{(p,\mu)}(t)\) on antenna port \(p\) for RIM-RS is defined by

    \(s_{l}^{(p,\mu)}(t) = \sum\limits_{k = 0}^{L_{\text{R}\text{IM}} - 1}a_{k}^{(p,\text{RIM})}e^{j2\pi{({k + k_{1}})}\Delta f_{\text{R}\text{IM}}{({t - N_{\text{CP}}^{\text{R}\text{IM}}T_{\text{c}} - t_{\text{start}\text{,}l_{0}}^{\mu}})}}\)

where

\[t_{\text{start}\text{,}l_{0}}^{\text{RIM}} \leq t < t_{\text{start}\text{,}l_{0}}^{\text{RIM}} + \left( {N_{\text{u}}^{\text{RIM}} + N_{\text{CP}}^{\text{RIM}}} \right)T_{\text{c}}\]

\[N_{\text{u}}^{\text{RIM}} = 2 \cdot 2048\kappa \cdot 2^{- \mu}\]

\[N_{\text{CP}}^{\text{RIM}} = N_{\text{CP,}l_{0}}^{\text{RIM}} + N_{\text{CP,}\bar{l}}^{\text{RIM}}\]

\[\bar{l} = \begin{cases} 0 & {\text{if}l_{0} = N_{\text{symb}}^{\text{slot}} - 1} \\ {l_{0} + 1} & \text{otherwise} \end{cases}\]

and

-    \(\Delta f_{\text{R}\text{IM}} = 15 \cdot 2^{\mu}\text{kHz}\) where \(\mu \in \left\{ 0,1 \right\}\) is the subcarrier spacing configuration for the RIM-RS;

-    \(k_{1}\) is the starting frequency offset of the RIM-RS as given by clause 7.4.1.6.4.3;

-    \(L_{\text{R}\text{IM}} = 12N_{\text{RB}}^{\text{RIM}}\) is the length of the RIM-RS sequence where \(N_{\text{RB}}^{\text{RIM}}\) is the bandwidth of the RIM-RS in resource blocks;

-    \(l_{0}\) is the starting symbol given by clause 7.4.1.6.3;

-    \(t_{\text{start}\text{,}l_{0}}^{\text{RIM}} = t_{\text{start}\text{,}l}^{\mu}\) is given by clause 5.3.1 with \({l = l}_{0}\);

-    \(N_{\text{CP,}l_{0}}^{\text{RIM}} = N_{\text{CP}\text{,}l}^{\mu}\) is given by clause 5.3.1 with \({l = l}_{0}\).

5.4     Modulation and upconversion #

Modulation and upconversion to the carrier frequency \(f_{0}\) of the complex-valued OFDM baseband signal for antenna port \(p\), subcarrier spacing configuration \(\mu\), and OFDM symbol \(l\) in a subframe assumed to start at \(t=0\) is given by

-    for PRACH

    \(\text{Re}\left\{ {s_{l}^{(p,\mu)}(t)e^{j2\pi f_{0}t}} \right\}\)

-    for RIM-RS

    \(\text{Re}\left\{ {s_{l}^{(p,\mu)}(t)e^{j2\pi f_{0}^{\text{RIM}}{({t - t_{{\text{start},l}_{0}}^{\mu} - N_{\text{CP}}^{\text{RIM}}T_{\text{c}}})}}} \right\}\)

where \(f_{0}^{\text{RIM}}\) is the configured reference point for RIM-RS;

-    for all other channels and signals

    \(\mathrm{Re}\left\{ s_{l}^{(p,\mu)}(t)\cdot e^{j 2\pi f_{0}\left(t - t_{start,l}^{\mu} - N_{CP}^{\mu} T_{c}\right)} \right\}\)

NOTE:    For the uplink, the signal \(s_{l}^{(p,\mu)}(t)\) and the baseband signals part thereof should be filtered per UE implementation, as required, to meet the minimum requirements as specified in [14, 38.101-1], [15, 38.101-2], and [16, 38.101-5] for the respective frequency range.

6     Uplink #

6 .1    Overview #

6 .1.1    Overview of physical channels #

An uplink physical channel corresponds to a set of resource elements carrying information originating from higher layers. The following uplink physical channels are defined:

-    Physical Uplink Shared Channel, PUSCH

-    Physical Uplink Control Channel, PUCCH

-    Physical Random Access Channel, PRACH

6 .1.2    Overview of physical signals #

An uplink physical signal is used by the physical layer but does not carry information originating from higher layers. The following uplink physical signals are defined:

-    Demodulation reference signals, DM-RS

-    Phase-tracking reference signals, PT-RS

-    Sounding reference signal, SRS

6 .2    Physical resources #

The frame structure and physical resources the UE shall use when transmitting in the uplink transmissions are defined in Clause 4.

The following antenna ports are defined for the uplink:

-    Antenna ports starting with 0 for demodulation reference signals for PUSCH

-    Antenna ports starting with 1000 for SRS, PUSCH

-    Antenna ports starting with 2000 for PUCCH

-    Antenna port 4000 for PRACH

If PUSCH repetition Type B as described in clause 6.1 of [6, TS38.214] is applied to a physical channel, the UE transmission shall be such that the channel over which a symbol on the antenna port used for uplink transmission is conveyed can be inferred from the channel over which another symbol on the same antenna port is conveyed if the two symbols correspond to the same actual repetition of a PUSCH transmission with repetition Type B.

If intra-slot frequency hopping is not enabled for a physical channel and PUSCH repetition Type B is not applied to the physical channel, the UE transmission shall be such that the channel over which a symbol on the antenna port used for uplink transmission is conveyed can be inferred from the channel over which another symbol on the same antenna port is conveyed if the two symbols correspond to the same slot.

If intra-slot frequency hopping is enabled for a physical channel, the UE transmission shall be such that the channel over which a symbol on the antenna port used for uplink transmission is conveyed can be inferred from the channel over which another symbol on the same antenna port is conveyed only if the two symbols correspond to the same frequency hop, regardless of whether the frequency hop distance is zero or not.

If DM-RS bundling is applied to PUSCH and/or PUCCH repetitions and/or transport-block processing over multiple="multiple" slots as described in clause 6.1.7 of [6, 38.214], the UE transmission shall be such that the channel over which a symbol on the antenna port used for uplink transmission is conveyed can be inferred from the channel over which another symbol on the same antenna port is conveyed if the two symbols are transmitted within the same actual time-domain window.

If inter-slot OCC is applied to PUSCH as described in clause XXX of [6, 38.214], the UE transmission shall be such that the channel over which a symbol on the antenna port used for uplink transmission is conveyed can be inferred from the channel over which another symbol on the same antenna port is conveyed if the two symbols are transmitted on slots within the same orthogonal cover code.

6.2.1     Muting resource #

A muting resource corresponds to a set of resource elements, defined by OFDM symbols in the time domain and a comb-2 in the frequency domain. The position in the slot of the up to two OFDM symbols, and the comb offset relative to the lowest indexed resource element of the PUSCH allocation, are given by the higher-layer parameters symbolPos and combOffset, respectively, in the PUSCH-MutingResources information element.

The UE is not expected to be configured with a muting resource within which resource elements overlap in time and frequency with a resource element used for PUSCH PT-RS when transform precoding is not enabled.

The UE shall ignore any resource elements of a muting resource that overlaps in time with an OFDM symbol used for any of

-    PUSCH DM-RS

-    PT-RS when transform precoding is enabled

6 .3    Physical channels #

6 .3.1.1    Scrambling #

Up to two codewords \(q \in \left\{ 0,1 \right\}\) can be transmitted. In case of single-codeword transmission, \(q = 0\).

For each codeword, the block of bits \(b^{(q)}(0),\ldots,b^{(q)}\left( {M_{\text{bit}}^{(q)} - 1} \right)\), where \(M_{\text{bit}}^{(q)}\) is the number of bits in codeword \(q\) transmitted on the physical channel, shall be scrambled prior to modulation, resulting in a block of scrambled bits \({\overset{\sim}{b}}^{(q)}(0),\ldots,{\overset{\sim}{b}}^{(q)}\left( {M_{\text{bit}}^{(q)} - 1} \right)\) according to the following pseudo code

Set i = 0

while \(i < M_{\text{bit}}^{(q)}\)

if \(b^{(q)}(i) = x\)    // UCI placeholder bits

\({\overset{\sim}{b}}^{(q)}(i)\) =1

else

if \(b^{(q)}(i) = y\)    // UCI placeholder bits

\({\overset{\sim}{b}}^{(q)}(i)\) = \({\overset{\sim}{b}}^{(q)}\left( {i - 1} \right)\)

else

\({\overset{\sim}{b}}^{(q)}(i)\) = (\(b^{(q)}(i)\) +\(\left. c^{(q)}(i) \right)mod2\)

end if

end if

i = i + 1

end while

where x and y are tags defined in [4, TS 38.212] and where the scrambling sequence \(c^{(q)}(i)\) is given by clause 5.2.1. The scrambling sequence generator shall be initialized with

\[c_{\text{init}} = \begin{cases} {n_{\text{RNTI}} \bullet 2^{16} + n_{\text{RAPID}} \bullet 2^{10} + n_{\text{ID}}} & \text{for msgA on PUSCH} \\ {n_{\text{RNTI}} \bullet 2^{15} + q \bullet 2^{14} + n_{\text{ID}}} & \text{otherwise} \end{cases}\]

where

-    \(n_{\text{ID}} \in \left\{ {0,1,\ldots,1023} \right\}\) equals the higher-layer parameter dataScramblingIdentityPUSCH if configured and the RNTI equals the C-RNTI, MCS-C-RNTI, SP-CSI-RNTI or CS-RNTI, and the transmission is not scheduled using DCI format 0_0 in a common search space;

-    \(n_{\text{ID}} \in \left\{ {0,1,\ldots,1023} \right\}\) equals the higher-layer parameter msgA-DataScramblingIndex if configured and the PUSCH transmission is triggered by a Type-2 random access procedure as described in clause 8.1A of [5, TS 38.213];

-    \(n_{\text{ID}} = N_{\text{ID}}^{\text{cell}}\) otherwise

-    \(n_{\text{RAPID}}\) is the index of the random-access preamble transmitted for msgA as described in clause 5.1.3A of [11, TS 38.321]

and where \(n_{\mathrm{RNTI}}\) equals the RA-RNTI for msgA and otherwise corresponds to the RNTI associated with the PUSCH transmission as described in clause 6.1 of [6, TS 38.214] and clause 8.3 of [5, TS 38.213].

6 .3.1.2    Modulation #

For each codeword \(q\), the block of scrambled bits \({\overset{\sim}{b}}^{(q)}(0),\ldots,{\overset{\sim}{b}}^{(q)}\left( {M_{\text{bit}}^{(q)} - 1} \right)\) shall be modulated as described in clause 5.1 using one of the modulation schemes in Table 6.3.1.2-1, resulting in a block of complex-valued modulation symbols \({\overset{\sim}{d}}^{(q)}(0),\ldots,{\overset{\sim}{d}}^{(q)}\left( M_{\text{symb}}^{(q)} - 1 \right)\).

Table 6.3.1.2-1: Supported modulation schemes.

Transform precoding disabled

Transform precoding enabled

Modulation scheme

Modulation order \(Q_m\)

Modulation scheme

Modulation order \(Q_m\)

 

 

π/2-BPSK

1

QPSK

2

QPSK

2

16QAM

4

16QAM

4

64QAM

6

64QAM

6

256QAM

8

256QAM

8

 

6.3.1.2a     Inter-slot cover code #

The block of complex-valued modulation symbols \({\overset{\sim}{d}}^{(q)}(0),\ldots,{\overset{\sim}{d}}^{(q)}\left( M_{\text{symb}}^{(q)} - 1 \right)\) shall be multiplied with the quantity \(w_{i}\) to form the block of complex-valued modulation symbols \(d^{(q)}(0),\ldots,d^{(q)}\left( M_{\text{symb}}^{(q)} - 1 \right)\).

If the UE transmits PUSCH using repetition type A with OCC

-    the quantity \(w_{i}\) is obtained according to clause 6.1.2.1 of [6, 38.214];

otherwise,

-    \(w_{i} = 1\).

6 .3.1.3    Layer mapping #

The complex-valued modulation symbols for each of the codewords to be transmitted shall be mapped onto up to four layers according to Table 7.3.1.3-1. Complex-valued modulation symbols \(d^{(q)}(0),\ldots,d^{(q)}\left( {M_{\text{symb}}^{(q)} - 1} \right)\) for codeword \(q\) shall be mapped onto the layers \(x(i) = \begin{bmatrix} {x^{(0)}(i)} & \ldots & {x^{({\upsilon - 1})}(i)} \end{bmatrix}^{\text{T}}\), \(i = 0,1,\ldots,M_{\text{symb}}^{\text{layer}} - 1\) where \(\upsilon\) is the number of layers and \(M_{\text{symb}}^{\text{layer}}\) is the number of modulation symbols per layer.

6 .3.1.4    Transform precoding #

If transform precoding is not enabled according to 6.1.3 of [6, TS38.214], \(y^{(\lambda)}(i) = x^{(\lambda)}(i)\) for each layer \(\lambda = 0,1,\ldots,\nu - 1\).

If transform precoding is enabled according to 6.1.3 of [6, TS38.214], \(\upsilon = 1\) and \(\tilde{x}^{(0)}(i)\) depends on the configuration of phase-tracking reference signals.

If the procedure in [6, TS 38.214] indicates that phase-tracking reference signals are not being used, the block of complex-valued symbols \(x^{(0)}(0),\ldots,x^{(0)}\left( {M_{\text{symb}}^{\text{layer}} - 1} \right)\) for the single layer \(\lambda = 0\) shall be divided into sets, each corresponding to one OFDM symbol and where set \(l\) contains \(M_{\text{sc},l}^{\text{PUSCH}}\) symbols and is mapped to the complex-valued symbols \({\overset{\sim}{x}}_{l}^{(0)}\left( i^{'} \right)\), corresponding to OFDM symbol \(l\) prior to transform precoding, with \(i' \in \left\{ {0,1,\ldots,M_{\text{sc},l}^{\text{PUSCH}} - 1} \right\}\).

If the procedure in [6, TS 38.214] indicates that phase-tracking reference signals are being used, the block of complex-valued symbols \(x^{(0)}(0),\ldots,x^{(0)}\left( {M_{\text{symb}}^{\text{layer}} - 1} \right)\) shall be divided into sets, each set corresponding to one OFDM symbol, and where set \(l\) contains \(M_{\text{sc}\text{,}l}^{\text{PUSCH}} - \varepsilon_{l}N_{\text{samp}}^{\text{group}}N_{\text{group}}^{\text{PTRS}}\) symbols and is mapped to the complex-valued symbols \({\overset{\sim}{x}}_{l}^{(0)}\left( i^{'} \right)\) corresponding to OFDM symbol \(l\) prior to transform precoding, with \(i' \in \left\{ {0,1,\ldots,M_{\text{sc},l}^{\text{PUSCH}} - 1} \right\}\) and \(i' \neq m\). The index \(m\) of PT-RS samples in set \(l\), the number of samples per PT-RS group \(N_{\text{samp}}^{\text{group}}\), and the number of PT-RS groups \(N_{\text{group}}^{\text{PT-RS}}\) are defined in clause 6.4.1.2.2.2. The quantity \(\varepsilon_l = 1\) when OFDM symbol \(l\) contains one or more PT-RS samples, otherwise \(\varepsilon_l = 0\).

Transform precoding shall be applied according to

    \({\overset{\sim}{y}}_{l}^{(0)}(k){} = \frac{1}{\sqrt[{}]{M_{\text{sc,}\text{l}}^{\text{PUSCH}}}}\sum\limits_{i = 0}^{M_{\text{sc,}\text{l}}^{\text{PUSCH}} - 1}{{\overset{\sim}{x}}_{l}^{(0)}(i)e^{- j\frac{2\pi ik}{M_{\text{sc,}\text{l}}^{\text{PUSCH}}}}}\)

    \(k{} = 0,\ldots,M_{\text{sc,}\text{l}}^{\text{PUSCH}} - 1\)

resulting in a set of blocks of complex-valued symbols \({\overset{\sim}{y}}_{l}^{(0)}(0),\ldots,{\overset{\sim}{y}}_{l}^{(0)}\left( M_{\text{sc,}\text{l}}^{\text{PUSCH}} - 1 \right)\) that shall be concatenated in order of increasing \(l\) to form \(y^{(0)}(0),\ldots,y^{(0)}\left( {\overset{\sim}{M}}_{\text{symb}}^{\text{layer}} - 1 \right)\). The total number of modulations symbols \({\overset{\sim}{M}}_{\text{symb}}^{\text{layer}}\) equals \(M_{\text{symb}}^{\text{layer}}\) with any PT-RS samples added.

The variable\(M_{sc}^{\mathrm{PUSCH}} = M_{RB}^{\mathrm{PUSCH}} \cdot N_{sc}^{\mathrm{RB}}\), where \(M_{RB}^{\text{PUSCH}}\) represents the bandwidth of the PUSCH in terms of resource blocks, and shall fulfil

    \(M_{\mathrm{RB}}^{\mathrm{PUSCH}} = 2^{a_2}\cdot 3^{a_3}\cdot 5^{a_5}\)

where \(a_2, a_3, a_5\) is a set of non-negative integers.

The variable \(M_{\text{sc,}\text{l}}^{\text{PUSCH}}\) equals \(M_{\text{sc}}^{\text{PUSCH}}/2\) when OFDM symbol \(l\) is occupied by a muting resource, otherwise \(M_{\text{sc,}\text{l}}^{\text{PUSCH}} = M_{\text{sc}}^{\text{PUSCH}}\).

6 .3.1.5    Precoding #

The block of vectors \(\begin{bmatrix} {y^{(0)}(i)} & \ldots & {y^{({\upsilon - 1})}(i)} \end{bmatrix}^{\text{T}}\) shall be precoded according to

\[\begin{bmatrix} {z^{(p_{0})}(i)} \\ \vdots \\ {z^{(p_{\rho - 1})}(i)} \end{bmatrix} = W\begin{bmatrix} {y^{(0)}(i)} \\ \vdots \\ {y^{({\upsilon - 1})}(i)} \end{bmatrix}\]

where \(i = 0,1,\ldots,M_{\text{symb}}^{\text{ap}} - 1\), \(M_{\text{symb}}^{\text{ap}} = {\overset{\sim}{M}}_{\text{symb}}^{\text{layer}}\). The set of antenna ports \(\left\{ {p_{0},\ldots,p_{\rho - 1}} \right\}\) shall be determined according to the procedure in [6, TS 38.214].

For non-codebook-based transmission, the precoding matrix \(W\) equals the identity matrix.

For codebook-based transmission, the precoding matrix \(W\) depends on the number of antenna ports used for the transmission:

-    for single-layer transmission on a single antenna port, \(W = 1\);

-    for transmissions using 2, or 4 antenna ports, \(W\) is given by Tables 6.3.1.5-1 to 6.3.1.5-7;

-    for transmissions using 3 antenna ports when 4portSRS_3TX is configured, \(W\) is given by Tables 6.3.1.5-48 to 6.3.1.5-50;

-    for transmissions using 8 antenna ports, \(W\) is given by

\[W_{f(i)} = {W'}_{i}\]

    where

-    the subscripts \(i\) and \(f(i)\) denote the row of the respective matrix;

-    \(f(i)\) is given by Table 6.3.1.5-8;

-    the intermediate precoding matrix \(W'\) is given by Tables 6.3.1.5-9 to 6.3.1.5-24, 6.3.1.5-29 to 6.3.1.5-36, and 6.3.1.5-39 to 6.3.1.5-47 with \(0_{m \times n}\) representing the all-zero matrix with \(m\) rows and \(n\) columns;

-    the submatrices \({\bar{W}}_{m,n}\) are given by Tables 6.3.1.5-25 to 6.3.1.5-28 and 6.3.1.5-37 to 6.3.1.5-38.

The TPMI index used in the tables above is obtained from the DCI scheduling the uplink transmission or the higher layer parameters according to the procedure in [6, TS 38.214].

When the higher-layer parameter txConfig is not configured, the precoding matrix \(W = 1\).

Table 6.3.1.5-1: Precoding matrix \(\mathbf{W}\) for single-layer transmission using two antenna ports.

TPMI index

\(W\)(ordered from left to right in increasing order of TPMI index)<br>

0 – 5

\(\frac{1}{\sqrt{2}}\begin{bmatrix}1\\0\end{bmatrix}\)

\(\frac{1}{\sqrt{2}}\begin{bmatrix}0\\1\end{bmatrix}\)

\(\frac{1}{\sqrt{2}}\begin{bmatrix}1\\1\end{bmatrix}\)

\(\frac{1}{\sqrt{2}}\begin{bmatrix}1\\-1\end{bmatrix}\)

\(\frac{1}{\sqrt{2}}\begin{bmatrix}1\\j\end{bmatrix}\)

\(\frac{1}{\sqrt{2}}\begin{bmatrix}1\\-j\end{bmatrix}\)

-

-

 

Table 6.3.1.5-2: Precoding matrix \(\mathbf{W}\) for single-layer transmission using four antenna ports with transform precoding enabled.

TPMI index

\(W\)(ordered from left to right in increasing order of TPMI index)<br>

0 – 7

\(\frac{1}{2}\begin{bmatrix}1\\0\\0\\0\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}0\\1\\0\\0\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}0\\0\\1\\0\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}0\\0\\0\\1\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\0\\1\\0\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\0\\-1\\0\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\0\\j\\0\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\0\\-j\\0\end{bmatrix}\)

8 – 15

\(\frac{1}{2}\begin{bmatrix}0\\1\\0\\1\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}0\\1\\0\\-1\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}0\\1\\0\\j\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}0\\1\\0\\-j\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\1\\1\\-1\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\1\\j\\j\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\1\\-1\\1\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\1\\-j\\-j\end{bmatrix}\)

16 – 23

\(\frac{1}{2}\begin{bmatrix}1\\ j\\ 1\\ j\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\ j\\ j\\ 1\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\ j\\ -1\\ -j\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\ j\\ -j\\ -1\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\-1\\1\\1\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\-1\\j\\-j\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\-1\\-1\\-1\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\-1\\-j\\j\end{bmatrix}\)

24 – 27

\(\frac{1}{2}\begin{bmatrix}1\\-j\\1\\-j\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\-j\\j\\-1\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\-j\\-1\\j\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\-j\\-j\\1\end{bmatrix}\)

-

-

-

-

 

Table 6.3.1.5-3: Precoding matrix \(\mathbf{W}\) for single-layer transmission using four antenna ports with transform precoding disabled.

TPMI index

\(W\)(ordered from left to right in increasing order of TPMI index)<br>

0 – 7

\(\frac{1}{2}\begin{bmatrix}1\\0\\0\\0\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}0\\1\\0\\0\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}0\\0\\1\\0\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}0\\0\\0\\1\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\0\\1\\0\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\0\\-1\\0\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\0\\j\\0\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\0\\-j\\0\end{bmatrix}\)

8 – 15

\(\frac{1}{2}\begin{bmatrix}0\\1\\0\\1\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}0\\1\\0\\-1\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}0\\1\\0\\j\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}0\\1\\0\\-j\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\1\\1\\1\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\1\\j\\j\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\[4pt]1\\[4pt]-1\\[4pt]-1\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\1\\-j\\-j\end{bmatrix}\)

16 – 23

\(\frac{1}{2}\begin{bmatrix}1\\j\\1\\j\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\ j\\ j\\ -1\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\ j\\ -1\\ -j\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\j\\-j\\1\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\-1\\1\\-1\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\-1\\j\\-j\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\-1\\-1\\1\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\-1\\-j\\j\end{bmatrix}\)

24 – 27

\(\frac{1}{2}\begin{bmatrix}1\\-j\\1\\-j\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\-j\\j\\1\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\-j\\-1\\j\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1\\-j\\j\\-1\end{bmatrix}\)

-

-

-

-

 

Table 6.3.1.5-4: Precoding matrix \(\mathbf{W}\) for two-layer transmission using two antenna ports with transform precoding disabled.

TPMI index

\(W\)(ordered from left to right in increasing order of TPMI index)<br>

0 – 2

\(\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1 & 1 \\ 1 & -1\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1 & 1 \\ j & -j\end{bmatrix}\)

-

 

Table 6.3.1.5-5: Precoding matrix \(\mathbf{W}\) for two-layer transmission using four antenna ports with transform precoding disabled.

TPMI index

\(W\)(ordered from left to right in increasing order of TPMI index)<br>

0 – 3

\(\frac{1}{2}\begin{bmatrix}1&0\\0&1\\0&0\\0&0\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1&0\\0&0\\0&1\\0&0\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1&0\\0&0\\0&0\\0&1\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}0&0\\1&0\\0&1\\0&0\end{bmatrix}\)

4 – 7

\(\frac{1}{2}\begin{bmatrix}0 & 0 \\ 1 & 0 \\ 0 & 0 \\ 0 & 1\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}0&0\\0&0\\1&0\\0&1\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1&0\\0&1\\1&0\\0&-j\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1&0\\0&1\\1&0\\0&j\end{bmatrix}\)

8 – 11

\(\frac{1}{2}\begin{bmatrix}1&0\\0&1\\-j&0\\0&1\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1&0\\0&1\\-j&0\\0&-1\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1 & 0\\0 & 1\\-1 & 0\\0 & -j\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1&0\\0&1\\-1&0\\0&j\end{bmatrix}\)

12 – 15

\(\frac{1}{2}\begin{bmatrix}1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & 1\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & -1\end{bmatrix}\)

\(\frac{1}{2\sqrt{2}}\begin{bmatrix}1&1\\1&1\\1&-1\\1&-1\end{bmatrix}\)

\(\frac{1}{2\sqrt{2}}\begin{bmatrix}1&1\\1&1\\j&-j\\j&-j\end{bmatrix}\)

16 – 19

\(\frac{1}{2\sqrt{2}}\begin{bmatrix}1&1\\ j&j\\ 1&-1\\ j&-j\end{bmatrix}\)

\(\frac{1}{2\sqrt{2}}\begin{bmatrix}1 & 1\\ j & j\\ j & -j\\ -1 & 1\end{bmatrix}\)

\(\frac{1}{2\sqrt{2}}\begin{bmatrix}1&1\\-1&-1\\1&-1\\-1&1\end{bmatrix}\)

\(\frac{1}{2\sqrt{2}}\begin{bmatrix}1 & 1\\ -1 & -1\\ j & -j\\ -j & j\end{bmatrix}\)

20 – 21

\(\frac{1}{2\sqrt{2}}\begin{bmatrix}1&1\\-j&-j\\1&-1\\-j&j\end{bmatrix}\)

\(\frac{1}{2\sqrt{2}}\begin{bmatrix}1 & 1\\ -j & -j\\ j & -j\\ 1 & -1\end{bmatrix}\)

-

-

 

Table 6.3.1.5-6: Precoding matrix \(\mathbf{W}\) for three-layer transmission using four antenna ports with transform precoding disabled.

TPMI index

\(W\)(ordered from left to right in increasing order of TPMI index)<br>

0 – 3

\(\frac{1}{2}\begin{bmatrix} 1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1\\ 0 & 0 & 0 \end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1&0&0\\0&1&0\\1&0&0\\0&0&1\end{bmatrix}\)

\(\frac{1}{2}\begin{bmatrix}1&0&0\\0&1&0\\-1&0&0\\0&0&1\end{bmatrix}\)

\(\frac{1}{2\sqrt{3}}\begin{bmatrix}1&1&1\\1&-1&1\\1&1&-1\\1&-1&-1\end{bmatrix}\)

4 – 6

\(\frac{1}{2\sqrt{3}}\begin{bmatrix}1&1&1\\1&-1&1\\j&j&-j\\j&-j&-j\end{bmatrix}\)

\(\frac{1}{2\sqrt{3}}\begin{bmatrix}1&1&1\\-1&1&-1\\1&1&-1\\-1&1&1\end{bmatrix}\)

\(\frac{1}{2\sqrt{3}}\begin{bmatrix} 1 & 1 & 1 \\ -1 & 1 & -1 \\ j & j & -j \\ -j & j & j \end{bmatrix}\)

-

 

Table 6.3.1.5-7: Precoding matrix \(\mathbf{W}\) for four-layer transmission using four antenna ports with transform precoding disabled.

TPMI index

\(W\)(ordered from left to right in increasing order of TPMI index)<br>

0 – 3

\(\frac{1}{2}\begin{bmatrix}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{bmatrix}\)

\(\frac{1}{2\sqrt{2}}\begin{bmatrix}1&1&0&0\\0&0&1&1\\1&-1&0&0\\0&0&1&-1\end{bmatrix}\)

\(\frac{1}{2\sqrt{2}}\begin{bmatrix}1&1&0&0\\0&0&1&1\\j&-j&0&0\\0&0&j&-j\end{bmatrix}\)

\(\frac{1}{4}\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & -1 & 1 & -1 \\ 1 & 1 & -1 & -1 \\ 1 & -1 & -1 & 1 \end{bmatrix}\)

4

\(\frac{1}{4}\begin{bmatrix}1&1&1&1\\1&-1&1&-1\\j&j&-j&-j\\j&-j&-j&j\end{bmatrix}\)

-

-

-

 

Table 6.3.1.5-8: The port mapping function \(\mathbf{f}\left( \mathbf{i} \right)\) for transmission using 8 antenna ports.

\[\mathbf{i}\]

Higher-layer parameter CodebookTypeUL

 

codebook1

codebook2

codebook3

codebook4

 

antenna port group

\[\mathbf{f}\left( \mathbf{i} \right)\]

antenna port group

\[\mathbf{f}\left( \mathbf{i} \right)\]

antenna port group

\[\mathbf{f}\left( \mathbf{i} \right)\]

antenna port group

\[\mathbf{f}\left( \mathbf{i} \right)\]

0

0

0

0

0

0

0

0

0

1

1

1

4

1

1

2

2

4

1

1

2

2

3

3

5

5

3

3

4

4

1

2

2

2

4

4

5

5

3

6

5

5

6

6

6

3

3

6

6

7

7

7

7

7

7

 

Table 6.3.1.5-9: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook1=ng1n4n1 and single-layer transmission using eight antenna ports.

TPMI index

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\) (ordered from left to right in increasing order of TPMI index)

0 – 7

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ 1 \\ 1 \\ 1 \\ j \\ j \\ j \\ j \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ 1 \\ 1 \\ 1 \\ {- 1} \\ {- 1} \\ {- 1} \\ {- 1} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ 1 \\ 1 \\ 1 \\ {- j} \\ {- j} \\ {- j} \\ {- j} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ j \\ {- 1} \\ {- j} \\ 1 \\ j \\ {- 1} \\ {- j} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ j \\ {- 1} \\ {- j} \\ j \\ {- 1} \\ {- j} \\ 1 \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ j \\ {- 1} \\ {- j} \\ {- 1} \\ {- j} \\ 1 \\ j \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ j \\ {- 1} \\ {- j} \\ {- j} \\ 1 \\ j \\ {- 1} \end{bmatrix}\]

8 – 15

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ {- 1} \\ 1 \\ {- 1} \\ 1 \\ {- 1} \\ 1 \\ {- 1} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ {- 1} \\ 1 \\ {- 1} \\ j \\ {- j} \\ j \\ {- j} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ {- 1} \\ 1 \\ {- 1} \\ {- 1} \\ 1 \\ {- 1} \\ 1 \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ {- 1} \\ 1 \\ {- 1} \\ {- j} \\ j \\ {- j} \\ j \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ {- j} \\ {- 1} \\ j \\ 1 \\ {- j} \\ {- 1} \\ j \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ {- j} \\ {- 1} \\ j \\ j \\ 1 \\ {- j} \\ {- 1} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ {- j} \\ {- 1} \\ j \\ {- 1} \\ j \\ 1 \\ {- j} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ {- j} \\ {- 1} \\ j \\ {- j} \\ {- 1} \\ j \\ 1 \end{bmatrix}\]

 

Table 6.3.1.5-10: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook1=ng1n4n1 and two-layer transmission using eight antenna ports with transform precoding disabled.

TPMI index

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)(ordered from left to right in increasing order of TPMI index)

0 – 7

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ 1 & 1 \\ 1 & 1 \\ 1 & 1 \\ 1 & {- 1} \\ 1 & {- 1} \\ 1 & {- 1} \\ 1 & {- 1} \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ 1 & 1 \\ 1 & 1 \\ 1 & 1 \\ j & {- j} \\ j & {- j} \\ j & {- j} \\ j & {- j} \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ 1 & j \\ 1 & {- 1} \\ 1 & {- j} \\ 1 & {- 1} \\ 1 & {- j} \\ 1 & 1 \\ 1 & j \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ 1 & j \\ 1 & {- 1} \\ 1 & {- j} \\ j & {- j} \\ j & 1 \\ j & j \\ j & {- 1} \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ 1 & {- 1} \\ 1 & 1 \\ 1 & {- 1} \\ 1 & {- 1} \\ 1 & 1 \\ 1 & {- 1} \\ 1 & 1 \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ 1 & {- 1} \\ 1 & 1 \\ 1 & {- 1} \\ j & {- j} \\ j & j \\ j & {- j} \\ j & j \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ 1 & {- j} \\ 1 & {- 1} \\ 1 & j \\ 1 & {- 1} \\ 1 & j \\ 1 & 1 \\ 1 & {- j} \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ 1 & {- j} \\ 1 & {- 1} \\ 1 & j \\ j & {- j} \\ j & {- 1} \\ j & j \\ j & 1 \end{bmatrix}\]

8 – 15

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ j & j \\ {- 1} & {- 1} \\ {- j} & {- j} \\ 1 & {- 1} \\ j & {- j} \\ {- 1} & 1 \\ {- j} & j \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ j & j \\ {- 1} & {- 1} \\ {- j} & {- j} \\ j & {- j} \\ {- 1} & 1 \\ {- j} & j \\ 1 & {- 1} \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ j & {- 1} \\ {- 1} & 1 \\ {- j} & {- 1} \\ 1 & {- 1} \\ j & 1 \\ {- 1} & {- 1} \\ {- j} & 1 \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ j & {- 1} \\ {- 1} & 1 \\ {- j} & {- 1} \\ j & {- j} \\ {- 1} & j \\ {- j} & {- j} \\ 1 & j \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ j & {- j} \\ {- 1} & {- 1} \\ {- j} & j \\ 1 & {- 1} \\ j & j \\ {- 1} & 1 \\ {- j} & {- j} \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ j & {- j} \\ {- 1} & {- 1} \\ {- j} & j \\ j & {- j} \\ {- 1} & {- 1} \\ {- j} & j \\ 1 & 1 \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ j & 1 \\ {- 1} & 1 \\ {- j} & 1 \\ 1 & {- 1} \\ j & {- 1} \\ {- 1} & {- 1} \\ {- j} & {- 1} \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ j & 1 \\ {- 1} & 1 \\ {- j} & 1 \\ j & {- j} \\ {- 1} & {- j} \\ {- j} & {- j} \\ 1 & {- j} \end{bmatrix}\]

16 – 23

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- 1} & {- 1} \\ 1 & 1 \\ {- 1} & {- 1} \\ 1 & {- 1} \\ {- 1} & 1 \\ 1 & {- 1} \\ {- 1} & 1 \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- 1} & {- 1} \\ 1 & 1 \\ {- 1} & {- 1} \\ j & {- j} \\ {- j} & j \\ j & {- j} \\ {- j} & j \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- 1} & {- j} \\ 1 & {- 1} \\ {- 1} & j \\ 1 & {- 1} \\ {- 1} & j \\ 1 & 1 \\ {- 1} & {- j} \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- 1} & {- j} \\ 1 & {- 1} \\ {- 1} & j \\ j & {- j} \\ {- j} & {- 1} \\ j & j \\ {- j} & 1 \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- 1} & 1 \\ 1 & 1 \\ {- 1} & 1 \\ 1 & {- 1} \\ {- 1} & {- 1} \\ 1 & {- 1} \\ {- 1} & {- 1} \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- 1} & 1 \\ 1 & 1 \\ {- 1} & 1 \\ j & {- j} \\ {- j} & {- j} \\ j & {- j} \\ {- j} & {- j} \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- 1} & j \\ 1 & {- 1} \\ {- 1} & {- j} \\ 1 & {- 1} \\ {- 1} & {- j} \\ 1 & 1 \\ {- 1} & j \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- 1} & j \\ 1 & {- 1} \\ {- 1} & {- j} \\ j & {- j} \\ {- j} & 1 \\ j & j \\ {- j} & {- 1} \end{bmatrix}\]

24 – 31

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- j} & {- j} \\ {- 1} & {- 1} \\ j & j \\ 1 & {- 1} \\ {- j} & j \\ {- 1} & 1 \\ j & {- j} \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- j} & {- j} \\ {- 1} & {- 1} \\ j & j \\ j & {- j} \\ 1 & {- 1} \\ {- j} & j \\ {- 1} & 1 \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- j} & 1 \\ {- 1} & 1 \\ j & 1 \\ 1 & {- 1} \\ {- j} & {- 1} \\ {- 1} & {- 1} \\ j & {- 1} \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- j} & 1 \\ {- 1} & 1 \\ j & 1 \\ j & {- j} \\ 1 & {- j} \\ {- j} & {- j} \\ {- 1} & {- j} \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- j} & j \\ {- 1} & {- 1} \\ j & {- j} \\ 1 & {- 1} \\ {- j} & {- j} \\ {- 1} & 1 \\ j & j \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- j} & j \\ {- 1} & {- 1} \\ j & {- j} \\ j & {- j} \\ 1 & 1 \\ {- j} & j \\ {- 1} & {- 1} \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- j} & {- 1} \\ {- 1} & 1 \\ j & {- 1} \\ 1 & {- 1} \\ {- j} & 1 \\ {- 1} & {- 1} \\ j & 1 \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- j} & {- 1} \\ {- 1} & 1 \\ j & {- 1} \\ j & {- j} \\ 1 & j \\ {- j} & {- j} \\ {- 1} & j \end{bmatrix}\]

 

Table 6.3.1.5-11: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook1=ng1n4n1 and three-layer transmission using eight antenna ports with transform precoding disabled.

TPMI index

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)(ordered from left to right in increasing order of TPMI index)

0 – 3

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ 1 & j & 1 \\ 1 & {- 1} & 1 \\ 1 & {- j} & 1 \\ 1 & 1 & {- 1} \\ 1 & j & {- 1} \\ 1 & {- 1} & {- 1} \\ 1 & {- j} & {- 1} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ 1 & j & 1 \\ 1 & {- 1} & 1 \\ 1 & {- j} & 1 \\ j & j & {- j} \\ j & {- 1} & {- j} \\ j & {- j} & {- j} \\ j & 1 & {- j} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ 1 & {- 1} & 1 \\ 1 & 1 & 1 \\ 1 & {- 1} & 1 \\ 1 & 1 & {- 1} \\ 1 & {- 1} & {- 1} \\ 1 & 1 & {- 1} \\ 1 & {- 1} & {- 1} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ 1 & {- 1} & 1 \\ 1 & 1 & 1 \\ 1 & {- 1} & 1 \\ j & j & {- j} \\ j & {- j} & {- j} \\ j & j & {- j} \\ j & {- j} & {- j} \end{bmatrix}\]

4 – 7

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ 1 & {- j} & 1 \\ 1 & {- 1} & 1 \\ 1 & j & 1 \\ 1 & 1 & {- 1} \\ 1 & {- j} & {- 1} \\ 1 & {- 1} & {- 1} \\ 1 & j & {- 1} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ 1 & {- j} & 1 \\ 1 & {- 1} & 1 \\ 1 & j & 1 \\ j & j & {- j} \\ j & 1 & {- j} \\ j & {- j} & {- j} \\ j & {- 1} & {- j} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ j & {- 1} & j \\ {- 1} & 1 & {- 1} \\ {- j} & {- 1} & {- j} \\ 1 & 1 & {- 1} \\ j & {- 1} & {- j} \\ {- 1} & 1 & 1 \\ {- j} & {- 1} & j \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ j & {- 1} & j \\ {- 1} & 1 & {- 1} \\ {- j} & {- 1} & {- j} \\ j & j & {- j} \\ {- 1} & {- j} & 1 \\ {- j} & j & j \\ 1 & {- j} & {- 1} \end{bmatrix}\]

8 – 11

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ j & {- j} & j \\ {- 1} & {- 1} & {- 1} \\ {- j} & j & {- j} \\ 1 & 1 & {- 1} \\ j & {- j} & {- j} \\ {- 1} & {- 1} & 1 \\ {- j} & j & j \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ j & {- j} & j \\ {- 1} & {- 1} & {- 1} \\ {- j} & j & {- j} \\ j & j & {- j} \\ {- 1} & 1 & 1 \\ {- j} & {- j} & j \\ 1 & {- 1} & {- 1} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ j & 1 & j \\ {- 1} & 1 & {- 1} \\ {- j} & 1 & {- j} \\ 1 & 1 & {- 1} \\ j & 1 & {- j} \\ {- 1} & 1 & 1 \\ {- j} & 1 & j \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ j & 1 & j \\ {- 1} & 1 & {- 1} \\ {- j} & 1 & {- j} \\ j & j & {- j} \\ {- 1} & j & 1 \\ {- j} & j & j \\ 1 & j & {- 1} \end{bmatrix}\]

12 – 15

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ {- 1} & {- j} & {- 1} \\ 1 & {- 1} & 1 \\ {- 1} & j & {- 1} \\ 1 & 1 & {- 1} \\ {- 1} & {- j} & 1 \\ 1 & {- 1} & {- 1} \\ {- 1} & j & 1 \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ {- 1} & {- j} & {- 1} \\ 1 & {- 1} & 1 \\ {- 1} & j & {- 1} \\ j & j & {- j} \\ {- j} & 1 & j \\ j & {- j} & {- j} \\ {- j} & {- 1} & j \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ {- 1} & 1 & {- 1} \\ 1 & 1 & 1 \\ {- 1} & 1 & {- 1} \\ 1 & 1 & {- 1} \\ {- 1} & 1 & 1 \\ 1 & 1 & {- 1} \\ {- 1} & 1 & 1 \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ {- 1} & 1 & {- 1} \\ 1 & 1 & 1 \\ {- 1} & 1 & {- 1} \\ j & j & {- j} \\ {- j} & j & j \\ j & j & {- j} \\ {- j} & j & j \end{bmatrix}\]

16 – 19

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ {- 1} & j & {- 1} \\ 1 & {- 1} & 1 \\ {- 1} & {- j} & {- 1} \\ 1 & 1 & {- 1} \\ {- 1} & j & 1 \\ 1 & {- 1} & {- 1} \\ {- 1} & {- j} & 1 \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ {- 1} & j & {- 1} \\ 1 & {- 1} & 1 \\ {- 1} & {- j} & {- 1} \\ j & j & {- j} \\ {- j} & {- 1} & j \\ j & {- j} & {- j} \\ {- j} & 1 & j \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ {- j} & 1 & {- j} \\ {- 1} & 1 & {- 1} \\ j & 1 & j \\ 1 & 1 & {- 1} \\ {- j} & 1 & j \\ {- 1} & 1 & 1 \\ j & 1 & {- j} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ {- j} & 1 & {- j} \\ {- 1} & 1 & {- 1} \\ j & 1 & j \\ j & j & {- j} \\ 1 & j & {- 1} \\ {- j} & j & j \\ {- 1} & j & 1 \end{bmatrix}\]

20 – 23

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ {- j} & j & {- j} \\ {- 1} & {- 1} & {- 1} \\ j & {- j} & j \\ 1 & 1 & {- 1} \\ {- j} & j & j \\ {- 1} & {- 1} & 1 \\ j & {- j} & {- j} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ {- j} & j & {- j} \\ {- 1} & {- 1} & {- 1} \\ j & {- j} & j \\ j & j & {- j} \\ 1 & {- 1} & {- 1} \\ {- j} & {- j} & j \\ {- 1} & 1 & 1 \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ {- j} & {- 1} & {- j} \\ {- 1} & 1 & {- 1} \\ j & {- 1} & j \\ 1 & 1 & {- 1} \\ {- j} & {- 1} & j \\ {- 1} & 1 & 1 \\ j & {- 1} & {- j} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ {- j} & {- 1} & {- j} \\ {- 1} & 1 & {- 1} \\ j & {- 1} & j \\ j & j & {- j} \\ 1 & {- j} & {- 1} \\ {- j} & j & j \\ {- 1} & {- j} & 1 \end{bmatrix}\]

 

Table 6.3.1.5-12: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook1=ng1n4n1 and four-layer transmission using eight antenna ports with transform precoding disabled.

TPMI index

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)(ordered from left to right in increasing order of TPMI index)

0 – 3

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & j & 1 & j \\ 1 & {- 1} & 1 & {- 1} \\ 1 & {- j} & 1 & {- j} \\ 1 & 1 & {- 1} & {- 1} \\ 1 & j & {- 1} & {- j} \\ 1 & {- 1} & {- 1} & 1 \\ 1 & {- j} & {- 1} & j \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & j & 1 & j \\ 1 & {- 1} & 1 & {- 1} \\ 1 & {- j} & 1 & {- j} \\ j & j & {- j} & {- j} \\ j & {- 1} & {- j} & 1 \\ j & {- j} & {- j} & j \\ j & 1 & {- j} & {- 1} \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & {- 1} & 1 & {- 1} \\ 1 & 1 & 1 & 1 \\ 1 & {- 1} & 1 & {- 1} \\ 1 & 1 & {- 1} & {- 1} \\ 1 & {- 1} & {- 1} & 1 \\ 1 & 1 & {- 1} & {- 1} \\ 1 & {- 1} & {- 1} & 1 \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & {- 1} & 1 & {- 1} \\ 1 & 1 & 1 & 1 \\ 1 & {- 1} & 1 & {- 1} \\ j & j & {- j} & {- j} \\ j & {- j} & {- j} & j \\ j & j & {- j} & {- j} \\ j & {- j} & {- j} & j \end{bmatrix}\]

4 – 7

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & {- j} & 1 & {- j} \\ 1 & {- 1} & 1 & {- 1} \\ 1 & j & 1 & j \\ 1 & 1 & {- 1} & {- 1} \\ 1 & {- j} & {- 1} & j \\ 1 & {- 1} & {- 1} & 1 \\ 1 & j & {- 1} & {- j} \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & {- j} & 1 & {- j} \\ 1 & {- 1} & 1 & {- 1} \\ 1 & j & 1 & j \\ j & j & {- j} & {- j} \\ j & 1 & {- j} & {- 1} \\ j & {- j} & {- j} & j \\ j & {- 1} & {- j} & 1 \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ j & {- 1} & j & {- 1} \\ {- 1} & 1 & {- 1} & 1 \\ {- j} & {- 1} & {- j} & {- 1} \\ 1 & 1 & {- 1} & {- 1} \\ j & {- 1} & {- j} & 1 \\ {- 1} & 1 & 1 & {- 1} \\ {- j} & {- 1} & j & 1 \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ j & {- 1} & j & {- 1} \\ {- 1} & 1 & {- 1} & 1 \\ {- j} & {- 1} & {- j} & {- 1} \\ j & j & {- j} & {- j} \\ {- 1} & {- j} & 1 & j \\ {- j} & j & j & {- j} \\ 1 & {- j} & {- 1} & j \end{bmatrix}\]

8 – 11

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ j & {- j} & j & {- j} \\ {- 1} & {- 1} & {- 1} & {- 1} \\ {- j} & j & {- j} & j \\ 1 & 1 & {- 1} & {- 1} \\ j & {- j} & {- j} & j \\ {- 1} & {- 1} & 1 & 1 \\ {- j} & j & j & {- j} \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ j & {- j} & j & {- j} \\ {- 1} & {- 1} & {- 1} & {- 1} \\ {- j} & j & {- j} & j \\ j & j & {- j} & {- j} \\ {- 1} & 1 & 1 & {- 1} \\ {- j} & {- j} & j & j \\ 1 & {- 1} & {- 1} & 1 \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ j & 1 & j & 1 \\ {- 1} & 1 & {- 1} & 1 \\ {- j} & 1 & {- j} & 1 \\ 1 & 1 & {- 1} & {- 1} \\ j & 1 & {- j} & {- 1} \\ {- 1} & 1 & 1 & {- 1} \\ {- j} & 1 & j & {- 1} \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ j & 1 & j & 1 \\ {- 1} & 1 & {- 1} & 1 \\ {- j} & 1 & {- j} & 1 \\ j & j & {- j} & {- j} \\ {- 1} & j & 1 & {- j} \\ {- j} & j & j & {- j} \\ 1 & j & {- 1} & {- j} \end{bmatrix}\]

12 – 15

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ {- 1} & {- j} & {- 1} & {- j} \\ 1 & {- 1} & 1 & {- 1} \\ {- 1} & j & {- 1} & j \\ 1 & 1 & {- 1} & {- 1} \\ {- 1} & {- j} & 1 & j \\ 1 & {- 1} & {- 1} & 1 \\ {- 1} & j & 1 & {- j} \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ {- 1} & {- j} & {- 1} & {- j} \\ 1 & {- 1} & 1 & {- 1} \\ {- 1} & j & {- 1} & j \\ j & j & {- j} & {- j} \\ {- j} & 1 & j & {- 1} \\ j & {- j} & {- j} & j \\ {- j} & {- 1} & j & 1 \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ {- 1} & 1 & {- 1} & 1 \\ 1 & 1 & 1 & 1 \\ {- 1} & 1 & {- 1} & 1 \\ 1 & 1 & {- 1} & {- 1} \\ {- 1} & 1 & 1 & {- 1} \\ 1 & 1 & {- 1} & {- 1} \\ {- 1} & 1 & 1 & {- 1} \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ {- 1} & 1 & {- 1} & 1 \\ 1 & 1 & 1 & 1 \\ {- 1} & 1 & {- 1} & 1 \\ j & j & {- j} & {- j} \\ {- j} & j & j & {- j} \\ j & j & {- j} & {- j} \\ {- j} & j & j & {- j} \end{bmatrix}\]

16 – 19

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ {- 1} & j & {- 1} & j \\ 1 & {- 1} & 1 & {- 1} \\ {- 1} & {- j} & {- 1} & {- j} \\ 1 & 1 & {- 1} & {- 1} \\ {- 1} & j & 1 & {- j} \\ 1 & {- 1} & {- 1} & 1 \\ {- 1} & {- j} & 1 & j \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ {- 1} & j & {- 1} & j \\ 1 & {- 1} & 1 & {- 1} \\ {- 1} & {- j} & {- 1} & {- j} \\ j & j & {- j} & {- j} \\ {- j} & {- 1} & j & 1 \\ j & {- j} & {- j} & j \\ {- j} & 1 & j & {- 1} \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ {- j} & 1 & {- j} & 1 \\ {- 1} & 1 & {- 1} & 1 \\ j & 1 & j & 1 \\ 1 & 1 & {- 1} & {- 1} \\ {- j} & 1 & j & {- 1} \\ {- 1} & 1 & 1 & {- 1} \\ j & 1 & {- j} & {- 1} \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ {- j} & 1 & {- j} & 1 \\ {- 1} & 1 & {- 1} & 1 \\ j & 1 & j & 1 \\ j & j & {- j} & {- j} \\ 1 & j & {- 1} & {- j} \\ {- j} & j & j & {- j} \\ {- 1} & j & 1 & {- j} \end{bmatrix}\]

20 – 23

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ {- j} & j & {- j} & j \\ {- 1} & {- 1} & {- 1} & {- 1} \\ j & {- j} & j & {- j} \\ 1 & 1 & {- 1} & {- 1} \\ {- j} & j & j & {- j} \\ {- 1} & {- 1} & 1 & 1 \\ j & {- j} & {- j} & j \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ {- j} & j & {- j} & j \\ {- 1} & {- 1} & {- 1} & {- 1} \\ j & {- j} & j & {- j} \\ j & j & {- j} & {- j} \\ 1 & {- 1} & {- 1} & 1 \\ {- j} & {- j} & j & j \\ {- 1} & 1 & 1 & {- 1} \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ {- j} & {- 1} & {- j} & {- 1} \\ {- 1} & 1 & {- 1} & 1 \\ j & {- 1} & j & {- 1} \\ 1 & 1 & {- 1} & {- 1} \\ {- j} & {- 1} & j & 1 \\ {- 1} & 1 & 1 & {- 1} \\ j & {- 1} & {- j} & 1 \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ {- j} & {- 1} & {- j} & {- 1} \\ {- 1} & 1 & {- 1} & 1 \\ j & {- 1} & j & {- 1} \\ j & j & {- j} & {- j} \\ 1 & {- j} & {- 1} & j \\ {- j} & j & j & {- j} \\ {- 1} & {- j} & 1 & j \end{bmatrix}\]

 

Table 6.3.1.5-13: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook1=ng1n4n1 and five-layer transmission using eight antenna ports with transform precoding disabled.

TPMI index

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)(ordered from left to right in increasing order of TPMI index)

0 – 1

\[\frac{1}{2\sqrt[{}]{10}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & j & j & {- 1} \\ 1 & 1 & {- 1} & {- 1} & 1 \\ 1 & 1 & {- j} & {- j} & {- 1} \\ 1 & {- 1} & 1 & {- 1} & 1 \\ 1 & {- 1} & j & {- j} & {- 1} \\ 1 & {- 1} & {- 1} & 1 & 1 \\ 1 & {- 1} & {- j} & j & {- 1} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{10}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & j & j & {- 1} \\ 1 & 1 & {- 1} & {- 1} & 1 \\ 1 & 1 & {- j} & {- j} & {- 1} \\ j & {- j} & 1 & {- 1} & 1 \\ j & {- j} & j & {- j} & {- 1} \\ j & {- j} & {- 1} & 1 & 1 \\ j & {- j} & {- j} & j & {- 1} \end{bmatrix}\]

2 – 3

\[\frac{1}{2\sqrt[{}]{10}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 \\ j & j & {- 1} & {- 1} & {- j} \\ {- 1} & {- 1} & 1 & 1 & {- 1} \\ {- j} & {- j} & {- 1} & {- 1} & j \\ 1 & {- 1} & 1 & {- 1} & 1 \\ j & {- j} & {- 1} & 1 & {- j} \\ {- 1} & 1 & 1 & {- 1} & {- 1} \\ {- j} & j & {- 1} & 1 & j \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{10}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 \\ j & j & {- 1} & {- 1} & {- j} \\ {- 1} & {- 1} & 1 & 1 & {- 1} \\ {- j} & {- j} & {- 1} & {- 1} & j \\ j & {- j} & 1 & {- 1} & 1 \\ {- 1} & 1 & {- 1} & 1 & {- j} \\ {- j} & j & 1 & {- 1} & {- 1} \\ 1 & {- 1} & {- 1} & 1 & j \end{bmatrix}\]

4 – 5

\[\frac{1}{2\sqrt[{}]{10}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & {- j} & {- j} & 1 \\ 1 & 1 & {- 1} & {- 1} & 1 \\ {- 1} & {- 1} & j & j & 1 \\ 1 & {- 1} & 1 & {- 1} & 1 \\ {- 1} & 1 & {- j} & j & 1 \\ 1 & {- 1} & {- 1} & 1 & 1 \\ {- 1} & 1 & j & {- j} & 1 \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{10}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & {- j} & {- j} & 1 \\ 1 & 1 & {- 1} & {- 1} & 1 \\ {- 1} & {- 1} & j & j & 1 \\ j & {- j} & 1 & {- 1} & 1 \\ {- j} & j & {- j} & j & 1 \\ j & {- j} & {- 1} & 1 & 1 \\ {- j} & j & j & {- j} & 1 \end{bmatrix}\]

6 – 7

\[\frac{1}{2\sqrt[{}]{10}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 \\ {- j} & {- j} & 1 & 1 & j \\ {- 1} & {- 1} & 1 & 1 & {- 1} \\ j & j & 1 & 1 & {- j} \\ 1 & {- 1} & 1 & {- 1} & 1 \\ {- j} & j & 1 & {- 1} & j \\ {- 1} & 1 & 1 & {- 1} & {- 1} \\ j & {- j} & 1 & {- 1} & {- j} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{10}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 \\ {- j} & {- j} & 1 & 1 & j \\ {- 1} & {- 1} & 1 & 1 & {- 1} \\ j & j & 1 & 1 & {- j} \\ j & {- j} & 1 & {- 1} & 1 \\ 1 & {- 1} & 1 & {- 1} & j \\ {- j} & j & 1 & {- 1} & {- 1} \\ {- 1} & 1 & 1 & {- 1} & {- j} \end{bmatrix}\]

 

Table 6.3.1.5-14: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook1=ng1n4n1 and six-layer transmission using eight antenna ports with transform precoding disabled.

TPMI index

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)(ordered from left to right in increasing order of TPMI index)

0 – 1

\[\frac{1}{4\sqrt[{}]{3}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & j & j & {- 1} & {- 1} \\ 1 & 1 & {- 1} & {- 1} & 1 & 1 \\ 1 & 1 & {- j} & {- j} & {- 1} & {- 1} \\ 1 & {- 1} & 1 & {- 1} & 1 & {- 1} \\ 1 & {- 1} & j & {- j} & {- 1} & 1 \\ 1 & {- 1} & {- 1} & 1 & 1 & {- 1} \\ 1 & {- 1} & {- j} & j & {- 1} & 1 \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{3}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & j & j & {- 1} & {- 1} \\ 1 & 1 & {- 1} & {- 1} & 1 & 1 \\ 1 & 1 & {- j} & {- j} & {- 1} & {- 1} \\ j & {- j} & j & {- j} & 1 & {- 1} \\ j & {- j} & {- 1} & 1 & {- 1} & 1 \\ j & {- j} & {- j} & j & 1 & {- 1} \\ j & {- j} & 1 & {- 1} & {- 1} & 1 \end{bmatrix}\]

2 – 3

\[\frac{1}{4\sqrt[{}]{3}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 \\ j & j & {- 1} & {- 1} & {- j} & {- j} \\ {- 1} & {- 1} & 1 & 1 & {- 1} & {- 1} \\ {- j} & {- j} & {- 1} & {- 1} & j & j \\ 1 & {- 1} & 1 & {- 1} & 1 & {- 1} \\ j & {- j} & {- 1} & 1 & {- j} & j \\ {- 1} & 1 & 1 & {- 1} & {- 1} & 1 \\ {- j} & j & {- 1} & 1 & j & {- j} \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{3}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 \\ j & j & {- 1} & {- 1} & {- j} & {- j} \\ {- 1} & {- 1} & 1 & 1 & {- 1} & {- 1} \\ {- j} & {- j} & {- 1} & {- 1} & j & j \\ j & {- j} & j & {- j} & 1 & {- 1} \\ {- 1} & 1 & {- j} & j & {- j} & j \\ {- j} & j & j & {- j} & {- 1} & 1 \\ 1 & {- 1} & {- j} & j & j & {- j} \end{bmatrix}\]

4 – 5

\[\frac{1}{4\sqrt[{}]{3}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & {- j} & {- j} & 1 & 1 \\ 1 & 1 & {- 1} & {- 1} & 1 & 1 \\ {- 1} & {- 1} & j & j & 1 & 1 \\ 1 & {- 1} & 1 & {- 1} & 1 & {- 1} \\ {- 1} & 1 & {- j} & j & 1 & {- 1} \\ 1 & {- 1} & {- 1} & 1 & 1 & {- 1} \\ {- 1} & 1 & j & {- j} & 1 & {- 1} \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{3}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & {- j} & {- j} & 1 & 1 \\ 1 & 1 & {- 1} & {- 1} & 1 & 1 \\ {- 1} & {- 1} & j & j & 1 & 1 \\ j & {- j} & j & {- j} & 1 & {- 1} \\ {- j} & j & 1 & {- 1} & 1 & {- 1} \\ j & {- j} & {- j} & j & 1 & {- 1} \\ {- j} & j & {- 1} & 1 & 1 & {- 1} \end{bmatrix}\]

6 – 7

\[\frac{1}{4\sqrt[{}]{3}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 \\ {- j} & {- j} & 1 & 1 & j & j \\ {- 1} & {- 1} & 1 & 1 & {- 1} & {- 1} \\ j & j & 1 & 1 & {- j} & {- j} \\ 1 & {- 1} & 1 & {- 1} & 1 & {- 1} \\ {- j} & j & 1 & {- 1} & j & {- j} \\ {- 1} & 1 & 1 & {- 1} & {- 1} & 1 \\ j & {- j} & 1 & {- 1} & {- j} & j \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{3}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 \\ {- j} & {- j} & 1 & 1 & j & j \\ {- 1} & {- 1} & 1 & 1 & {- 1} & {- 1} \\ j & j & 1 & 1 & {- j} & {- j} \\ j & {- j} & j & {- j} & 1 & {- 1} \\ 1 & {- 1} & j & {- j} & j & {- j} \\ {- j} & j & j & {- j} & {- 1} & 1 \\ {- 1} & 1 & j & {- j} & {- j} & j \end{bmatrix}\]

 

Table 6.3.1.5-15: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook1=ng1n4n1 and seven-layer transmission using eight antenna ports with transform precoding disabled.

TPMI index

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)(ordered from left to right in increasing order of TPMI index)

0 – 1

\[\frac{1}{2\sqrt[{}]{14}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & j & {- 1} & {- 1} & {- j} & {- j} \\ 1 & 1 & {- 1} & 1 & 1 & {- 1} & {- 1} \\ 1 & 1 & {- j} & {- 1} & {- 1} & j & j \\ 1 & {- 1} & 1 & 1 & {- 1} & 1 & {- 1} \\ 1 & {- 1} & j & {- 1} & 1 & {- j} & j \\ 1 & {- 1} & {- 1} & 1 & {- 1} & {- 1} & 1 \\ 1 & {- 1} & {- j} & {- 1} & 1 & j & {- j} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{14}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & j & {- 1} & {- 1} & {- j} & {- j} \\ 1 & 1 & {- 1} & 1 & 1 & {- 1} & {- 1} \\ 1 & 1 & {- j} & {- 1} & {- 1} & j & j \\ j & {- j} & j & 1 & {- 1} & 1 & {- 1} \\ j & {- j} & {- 1} & {- 1} & 1 & {- j} & j \\ j & {- j} & {- j} & 1 & {- 1} & {- 1} & 1 \\ j & {- j} & 1 & {- 1} & 1 & j & {- j} \end{bmatrix}\]

2 – 3

\[\frac{1}{2\sqrt[{}]{14}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ j & j & {- 1} & {- j} & {- j} & 1 & 1 \\ {- 1} & {- 1} & 1 & {- 1} & {- 1} & 1 & 1 \\ {- j} & {- j} & {- 1} & j & j & 1 & 1 \\ 1 & {- 1} & 1 & 1 & {- 1} & 1 & {- 1} \\ j & {- j} & {- 1} & {- j} & j & 1 & {- 1} \\ {- 1} & 1 & 1 & {- 1} & 1 & 1 & {- 1} \\ {- j} & j & {- 1} & j & {- j} & 1 & {- 1} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{14}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ j & j & {- 1} & {- j} & {- j} & 1 & 1 \\ {- 1} & {- 1} & 1 & {- 1} & {- 1} & 1 & 1 \\ {- j} & {- j} & {- 1} & j & j & 1 & 1 \\ j & {- j} & j & 1 & {- 1} & 1 & {- 1} \\ {- 1} & 1 & {- j} & {- j} & j & 1 & {- 1} \\ {- j} & j & j & {- 1} & 1 & 1 & {- 1} \\ 1 & {- 1} & {- j} & j & {- j} & 1 & {- 1} \end{bmatrix}\]

 

Table 6.3.1.5-16: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook1=ng1n4n1 and eight-layer transmission using eight antenna ports with transform precoding disabled.

TPMI index

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)(ordered from left to right in increasing order of TPMI index)

0 – 1

\[\frac{1}{8}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & j & j & {- 1} & {- 1} & {- j} & {- j} \\ 1 & 1 & {- 1} & {- 1} & 1 & 1 & {- 1} & {- 1} \\ 1 & 1 & {- j} & {- j} & {- 1} & {- 1} & j & j \\ 1 & {- 1} & 1 & {- 1} & 1 & {- 1} & 1 & {- 1} \\ 1 & {- 1} & j & {- j} & {- 1} & 1 & {- j} & j \\ 1 & {- 1} & {- 1} & 1 & 1 & {- 1} & {- 1} & 1 \\ 1 & {- 1} & {- j} & j & {- 1} & 1 & j & {- j} \end{bmatrix}\]

\[\frac{1}{8}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & j & j & {- 1} & {- 1} & {- j} & {- j} \\ 1 & 1 & {- 1} & {- 1} & 1 & 1 & {- 1} & {- 1} \\ 1 & 1 & {- j} & {- j} & {- 1} & {- 1} & j & j \\ j & {- j} & j & {- j} & 1 & {- 1} & 1 & {- 1} \\ j & {- j} & {- 1} & 1 & {- 1} & 1 & {- j} & j \\ j & {- j} & {- j} & j & 1 & {- 1} & {- 1} & 1 \\ j & {- j} & 1 & {- 1} & {- 1} & 1 & j & {- j} \end{bmatrix}\]

2 – 3

\[\frac{1}{8}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ j & j & {- 1} & {- 1} & {- j} & {- j} & 1 & 1 \\ {- 1} & {- 1} & 1 & 1 & {- 1} & {- 1} & 1 & 1 \\ {- j} & {- j} & {- 1} & {- 1} & j & j & 1 & 1 \\ 1 & {- 1} & 1 & {- 1} & 1 & {- 1} & 1 & {- 1} \\ j & {- j} & {- 1} & 1 & {- j} & j & 1 & {- 1} \\ {- 1} & 1 & 1 & {- 1} & {- 1} & 1 & 1 & {- 1} \\ {- j} & j & {- 1} & 1 & j & {- j} & 1 & {- 1} \end{bmatrix}\]

\[\frac{1}{8}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ j & j & {- 1} & {- 1} & {- j} & {- j} & 1 & 1 \\ {- 1} & {- 1} & 1 & 1 & {- 1} & {- 1} & 1 & 1 \\ {- j} & {- j} & {- 1} & {- 1} & j & j & 1 & 1 \\ j & {- j} & j & {- j} & 1 & {- 1} & 1 & {- 1} \\ {- 1} & 1 & {- j} & j & {- j} & j & 1 & {- 1} \\ {- j} & j & j & {- j} & {- 1} & 1 & 1 & {- 1} \\ 1 & {- 1} & {- j} & j & j & {- j} & 1 & {- 1} \end{bmatrix}\]

 

Table 6.3.1.5-17: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook1=ng1n2n2 and single-layer transmission using eight antenna ports.

TPMI index

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)

(ordered from left to right in increasing order of TPMI index)

0 – 7

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ 1 \\ 1 \\ 1 \\ j \\ j \\ j \\ j \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ 1 \\ 1 \\ 1 \\ {- 1} \\ {- 1} \\ {- 1} \\ {- 1} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ 1 \\ 1 \\ 1 \\ {- j} \\ {- j} \\ {- j} \\ {- j} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ {- 1} \\ 1 \\ {- 1} \\ 1 \\ {- 1} \\ 1 \\ {- 1} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ {- 1} \\ 1 \\ {- 1} \\ j \\ {- j} \\ j \\ {- j} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ {- 1} \\ 1 \\ {- 1} \\ {- 1} \\ 1 \\ {- 1} \\ 1 \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ {- 1} \\ 1 \\ {- 1} \\ {- j} \\ j \\ {- j} \\ j \end{bmatrix}\]

8 – 15

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ 1 \\ {- 1} \\ {- 1} \\ 1 \\ 1 \\ {- 1} \\ {- 1} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ 1 \\ {- 1} \\ {- 1} \\ j \\ j \\ {- j} \\ {- j} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ 1 \\ {- 1} \\ {- 1} \\ {- 1} \\ {- 1} \\ 1 \\ 1 \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ 1 \\ {- 1} \\ {- 1} \\ {- j} \\ {- j} \\ j \\ j \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ {- 1} \\ {- 1} \\ 1 \\ 1 \\ {- 1} \\ {- 1} \\ 1 \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ {- 1} \\ {- 1} \\ 1 \\ j \\ {- j} \\ {- j} \\ j \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ {- 1} \\ {- 1} \\ 1 \\ {- 1} \\ 1 \\ 1 \\ {- 1} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 \\ {- 1} \\ {- 1} \\ 1 \\ {- j} \\ j \\ j \\ {- j} \end{bmatrix}\]

 

Table 6.3.1.5-18: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook1=ng1n2n2 and two-layer transmission using eight antenna ports with transform precoding disabled.

TPMI index

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)(ordered from left to right in increasing order of TPMI index)

0 – 7

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ 1 & 1 \\ 1 & 1 \\ 1 & 1 \\ 1 & {- 1} \\ 1 & {- 1} \\ 1 & {- 1} \\ 1 & {- 1} \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ 1 & 1 \\ 1 & 1 \\ 1 & 1 \\ j & {- j} \\ j & {- j} \\ j & {- j} \\ j & {- j} \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ 1 & 1 \\ 1 & {- 1} \\ 1 & {- 1} \\ 1 & {- 1} \\ 1 & {- 1} \\ 1 & 1 \\ 1 & 1 \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ 1 & 1 \\ 1 & {- 1} \\ 1 & {- 1} \\ j & {- j} \\ j & {- j} \\ j & j \\ j & j \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ 1 & {- 1} \\ 1 & 1 \\ 1 & {- 1} \\ 1 & {- 1} \\ 1 & 1 \\ 1 & {- 1} \\ 1 & 1 \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ 1 & {- 1} \\ 1 & 1 \\ 1 & {- 1} \\ j & {- j} \\ j & j \\ j & {- j} \\ j & j \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ 1 & {- 1} \\ 1 & {- 1} \\ 1 & 1 \\ 1 & {- 1} \\ 1 & 1 \\ 1 & 1 \\ 1 & {- 1} \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ 1 & {- 1} \\ 1 & {- 1} \\ 1 & 1 \\ j & {- j} \\ j & j \\ j & j \\ j & {- j} \end{bmatrix}\]

8 – 15

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- 1} & {- 1} \\ 1 & 1 \\ {- 1} & {- 1} \\ 1 & {- 1} \\ {- 1} & 1 \\ 1 & {- 1} \\ {- 1} & 1 \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- 1} & {- 1} \\ 1 & 1 \\ {- 1} & {- 1} \\ j & {- j} \\ {- j} & j \\ j & {- j} \\ {- j} & j \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- 1} & {- 1} \\ 1 & {- 1} \\ {- 1} & 1 \\ 1 & {- 1} \\ {- 1} & 1 \\ 1 & 1 \\ {- 1} & {- 1} \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- 1} & {- 1} \\ 1 & {- 1} \\ {- 1} & 1 \\ j & {- j} \\ {- j} & j \\ j & j \\ {- j} & {- j} \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- 1} & 1 \\ 1 & 1 \\ {- 1} & 1 \\ 1 & {- 1} \\ {- 1} & {- 1} \\ 1 & {- 1} \\ {- 1} & {- 1} \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- 1} & 1 \\ 1 & 1 \\ {- 1} & 1 \\ j & {- j} \\ {- j} & {- j} \\ j & {- j} \\ {- j} & {- j} \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- 1} & 1 \\ 1 & {- 1} \\ {- 1} & {- 1} \\ 1 & {- 1} \\ {- 1} & {- 1} \\ 1 & 1 \\ {- 1} & 1 \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- 1} & 1 \\ 1 & {- 1} \\ {- 1} & {- 1} \\ j & {- j} \\ {- j} & {- j} \\ j & j \\ {- j} & j \end{bmatrix}\]

16 – 23

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ 1 & 1 \\ {- 1} & {- 1} \\ {- 1} & {- 1} \\ 1 & {- 1} \\ 1 & {- 1} \\ {- 1} & 1 \\ {- 1} & 1 \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ 1 & 1 \\ {- 1} & {- 1} \\ {- 1} & {- 1} \\ j & {- j} \\ j & {- j} \\ {- j} & j \\ {- j} & j \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ 1 & 1 \\ {- 1} & 1 \\ {- 1} & 1 \\ 1 & {- 1} \\ 1 & {- 1} \\ {- 1} & {- 1} \\ {- 1} & {- 1} \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ 1 & 1 \\ {- 1} & 1 \\ {- 1} & 1 \\ j & {- j} \\ j & {- j} \\ {- j} & {- j} \\ {- j} & {- j} \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ 1 & {- 1} \\ {- 1} & {- 1} \\ {- 1} & 1 \\ 1 & {- 1} \\ 1 & 1 \\ {- 1} & 1 \\ {- 1} & {- 1} \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ 1 & {- 1} \\ {- 1} & {- 1} \\ {- 1} & 1 \\ j & {- j} \\ j & j \\ {- j} & j \\ {- j} & {- j} \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ 1 & {- 1} \\ {- 1} & 1 \\ {- 1} & {- 1} \\ 1 & {- 1} \\ 1 & 1 \\ {- 1} & {- 1} \\ {- 1} & 1 \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ 1 & {- 1} \\ {- 1} & 1 \\ {- 1} & {- 1} \\ j & {- j} \\ j & j \\ {- j} & {- j} \\ {- j} & j \end{bmatrix}\]

24 – 31

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- 1} & {- 1} \\ {- 1} & {- 1} \\ 1 & 1 \\ 1 & {- 1} \\ {- 1} & 1 \\ {- 1} & 1 \\ 1 & {- 1} \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- 1} & {- 1} \\ {- 1} & {- 1} \\ 1 & 1 \\ j & {- j} \\ {- j} & j \\ {- j} & j \\ j & {- j} \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- 1} & {- 1} \\ {- 1} & 1 \\ 1 & {- 1} \\ 1 & {- 1} \\ {- 1} & 1 \\ {- 1} & {- 1} \\ 1 & 1 \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- 1} & {- 1} \\ {- 1} & 1 \\ 1 & {- 1} \\ j & {- j} \\ {- j} & j \\ {- j} & {- j} \\ j & j \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- 1} & 1 \\ {- 1} & {- 1} \\ 1 & {- 1} \\ 1 & {- 1} \\ {- 1} & {- 1} \\ {- 1} & 1 \\ 1 & 1 \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- 1} & 1 \\ {- 1} & {- 1} \\ 1 & {- 1} \\ j & {- j} \\ {- j} & {- j} \\ {- j} & j \\ j & j \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- 1} & 1 \\ {- 1} & 1 \\ 1 & 1 \\ 1 & {- 1} \\ {- 1} & {- 1} \\ {- 1} & {- 1} \\ 1 & {- 1} \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 \\ {- 1} & 1 \\ {- 1} & 1 \\ 1 & 1 \\ j & {- j} \\ {- j} & {- j} \\ {- j} & {- j} \\ j & {- j} \end{bmatrix}\]

 

Table 6.3.1.5-19: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook1=ng1n2n2 and three-layer transmission using eight antenna ports with transform precoding disabled.

TPMI index

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)(ordered from left to right in increasing order of TPMI index)

0 – 3

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & {- 1} & 1 \\ 1 & {- 1} & 1 \\ 1 & 1 & {- 1} \\ 1 & 1 & {- 1} \\ 1 & {- 1} & {- 1} \\ 1 & {- 1} & {- 1} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & {- 1} & 1 \\ 1 & {- 1} & 1 \\ j & j & {- j} \\ j & j & {- j} \\ j & {- j} & {- j} \\ j & {- j} & {- j} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ 1 & {- 1} & 1 \\ 1 & 1 & 1 \\ 1 & {- 1} & 1 \\ 1 & 1 & {- 1} \\ 1 & {- 1} & {- 1} \\ 1 & 1 & {- 1} \\ 1 & {- 1} & {- 1} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ 1 & {- 1} & 1 \\ 1 & 1 & 1 \\ 1 & {- 1} & 1 \\ j & j & {- j} \\ j & {- j} & {- j} \\ j & j & {- j} \\ j & {- j} & {- j} \end{bmatrix}\]

4 – 7

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ 1 & {- 1} & 1 \\ 1 & {- 1} & 1 \\ 1 & 1 & 1 \\ 1 & 1 & {- 1} \\ 1 & {- 1} & {- 1} \\ 1 & {- 1} & {- 1} \\ 1 & 1 & {- 1} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ 1 & {- 1} & 1 \\ 1 & {- 1} & 1 \\ 1 & 1 & 1 \\ j & j & {- j} \\ j & {- j} & {- j} \\ j & {- j} & {- j} \\ j & j & {- j} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ {- 1} & {- 1} & {- 1} \\ 1 & {- 1} & 1 \\ {- 1} & 1 & {- 1} \\ 1 & 1 & {- 1} \\ {- 1} & {- 1} & 1 \\ 1 & {- 1} & {- 1} \\ {- 1} & 1 & 1 \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ {- 1} & {- 1} & {- 1} \\ 1 & {- 1} & 1 \\ {- 1} & 1 & {- 1} \\ j & j & {- j} \\ {- j} & {- j} & j \\ j & {- j} & {- j} \\ {- j} & j & j \end{bmatrix}\]

8 – 11

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ {- 1} & 1 & {- 1} \\ 1 & 1 & 1 \\ {- 1} & 1 & {- 1} \\ 1 & 1 & {- 1} \\ {- 1} & 1 & 1 \\ 1 & 1 & {- 1} \\ {- 1} & 1 & 1 \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ {- 1} & 1 & {- 1} \\ 1 & 1 & 1 \\ {- 1} & 1 & {- 1} \\ j & j & {- j} \\ {- j} & j & j \\ j & j & {- j} \\ {- j} & j & j \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ {- 1} & 1 & {- 1} \\ 1 & {- 1} & 1 \\ {- 1} & {- 1} & {- 1} \\ 1 & 1 & {- 1} \\ {- 1} & 1 & 1 \\ 1 & {- 1} & {- 1} \\ {- 1} & {- 1} & 1 \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ {- 1} & 1 & {- 1} \\ 1 & {- 1} & 1 \\ {- 1} & {- 1} & {- 1} \\ j & j & {- j} \\ {- j} & j & j \\ j & {- j} & {- j} \\ {- j} & {- j} & j \end{bmatrix}\]

12 – 15

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ {- 1} & 1 & {- 1} \\ {- 1} & 1 & {- 1} \\ 1 & 1 & {- 1} \\ 1 & 1 & {- 1} \\ {- 1} & 1 & 1 \\ {- 1} & 1 & 1 \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ {- 1} & 1 & {- 1} \\ {- 1} & 1 & {- 1} \\ j & j & {- j} \\ j & j & {- j} \\ {- j} & j & j \\ {- j} & j & j \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ 1 & {- 1} & 1 \\ {- 1} & {- 1} & {- 1} \\ {- 1} & 1 & {- 1} \\ 1 & 1 & {- 1} \\ 1 & {- 1} & {- 1} \\ {- 1} & {- 1} & 1 \\ {- 1} & 1 & 1 \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ 1 & {- 1} & 1 \\ {- 1} & {- 1} & {- 1} \\ {- 1} & 1 & {- 1} \\ j & j & {- j} \\ j & {- j} & {- j} \\ {- j} & {- j} & j \\ {- j} & j & j \end{bmatrix}\]

16 – 19

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ 1 & {- 1} & 1 \\ {- 1} & 1 & {- 1} \\ {- 1} & {- 1} & {- 1} \\ 1 & 1 & {- 1} \\ 1 & {- 1} & {- 1} \\ {- 1} & 1 & 1 \\ {- 1} & {- 1} & 1 \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ 1 & {- 1} & 1 \\ {- 1} & 1 & {- 1} \\ {- 1} & {- 1} & {- 1} \\ j & j & {- j} \\ j & {- j} & {- j} \\ {- j} & j & j \\ {- j} & {- j} & j \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ {- 1} & {- 1} & {- 1} \\ {- 1} & 1 & {- 1} \\ 1 & {- 1} & 1 \\ 1 & 1 & {- 1} \\ {- 1} & {- 1} & 1 \\ {- 1} & 1 & 1 \\ 1 & {- 1} & {- 1} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ {- 1} & {- 1} & {- 1} \\ {- 1} & 1 & {- 1} \\ 1 & {- 1} & 1 \\ j & j & {- j} \\ {- j} & {- j} & j \\ {- j} & j & j \\ j & {- j} & {- j} \end{bmatrix}\]

20 – 23

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ {- 1} & 1 & {- 1} \\ {- 1} & {- 1} & {- 1} \\ 1 & {- 1} & 1 \\ 1 & 1 & {- 1} \\ {- 1} & 1 & 1 \\ {- 1} & {- 1} & 1 \\ 1 & {- 1} & {- 1} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ {- 1} & 1 & {- 1} \\ {- 1} & {- 1} & {- 1} \\ 1 & {- 1} & 1 \\ j & j & {- j} \\ {- j} & j & j \\ {- j} & {- j} & j \\ j & {- j} & {- j} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ {- 1} & 1 & {- 1} \\ {- 1} & 1 & {- 1} \\ 1 & 1 & 1 \\ 1 & 1 & {- 1} \\ {- 1} & 1 & 1 \\ {- 1} & 1 & 1 \\ 1 & 1 & {- 1} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{6}}\begin{bmatrix} 1 & 1 & 1 \\ {- 1} & 1 & {- 1} \\ {- 1} & 1 & {- 1} \\ 1 & 1 & 1 \\ j & j & {- j} \\ {- j} & j & j \\ {- j} & j & j \\ j & j & {- j} \end{bmatrix}\]

 

Table 6.3.1.5-20: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook1=ng1n2n2 and four-layer transmission using eight antenna ports with transform precoding disabled.

TPMI index

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)(ordered from left to right in increasing order of TPMI index)

0 – 3

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ 1 & {- 1} & 1 & {- 1} \\ 1 & {- 1} & 1 & {- 1} \\ 1 & 1 & {- 1} & {- 1} \\ 1 & 1 & {- 1} & {- 1} \\ 1 & {- 1} & {- 1} & 1 \\ 1 & {- 1} & {- 1} & 1 \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ 1 & {- 1} & 1 & {- 1} \\ 1 & {- 1} & 1 & {- 1} \\ j & j & {- j} & {- j} \\ j & j & {- j} & {- j} \\ j & {- j} & {- j} & j \\ j & {- j} & {- j} & j \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & {- 1} & 1 & {- 1} \\ 1 & 1 & 1 & 1 \\ 1 & {- 1} & 1 & {- 1} \\ 1 & 1 & {- 1} & {- 1} \\ 1 & {- 1} & {- 1} & 1 \\ 1 & 1 & {- 1} & {- 1} \\ 1 & {- 1} & {- 1} & 1 \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & {- 1} & 1 & {- 1} \\ 1 & 1 & 1 & 1 \\ 1 & {- 1} & 1 & {- 1} \\ j & j & {- j} & {- j} \\ j & {- j} & {- j} & j \\ j & j & {- j} & {- j} \\ j & {- j} & {- j} & j \end{bmatrix}\]

4 – 7

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & {- 1} & 1 & {- 1} \\ 1 & {- 1} & 1 & {- 1} \\ 1 & 1 & 1 & 1 \\ 1 & 1 & {- 1} & {- 1} \\ 1 & {- 1} & {- 1} & 1 \\ 1 & {- 1} & {- 1} & 1 \\ 1 & 1 & {- 1} & {- 1} \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & {- 1} & 1 & {- 1} \\ 1 & {- 1} & 1 & {- 1} \\ 1 & 1 & 1 & 1 \\ j & j & {- j} & {- j} \\ j & {- j} & {- j} & j \\ j & {- j} & {- j} & j \\ j & j & {- j} & {- j} \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & {- 1} & {- 1} \\ 1 & {- 1} & 1 & {- 1} \\ {- 1} & 1 & {- 1} & 1 \\ 1 & 1 & {- 1} & {- 1} \\ {- 1} & {- 1} & 1 & 1 \\ 1 & {- 1} & {- 1} & 1 \\ {- 1} & 1 & 1 & {- 1} \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & {- 1} & {- 1} \\ 1 & {- 1} & 1 & {- 1} \\ {- 1} & 1 & {- 1} & 1 \\ j & j & {- j} & {- j} \\ {- j} & {- j} & j & j \\ j & {- j} & {- j} & j \\ {- j} & j & j & {- j} \end{bmatrix}\]

8 – 11

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ {- 1} & 1 & {- 1} & 1 \\ 1 & 1 & 1 & 1 \\ {- 1} & 1 & {- 1} & 1 \\ 1 & 1 & {- 1} & {- 1} \\ {- 1} & 1 & 1 & {- 1} \\ 1 & 1 & {- 1} & {- 1} \\ {- 1} & 1 & 1 & {- 1} \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ {- 1} & 1 & {- 1} & 1 \\ 1 & 1 & 1 & 1 \\ {- 1} & 1 & {- 1} & 1 \\ j & j & {- j} & {- j} \\ {- j} & j & j & {- j} \\ j & j & {- j} & {- j} \\ {- j} & j & j & {- j} \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ {- 1} & 1 & {- 1} & 1 \\ 1 & {- 1} & 1 & {- 1} \\ {- 1} & {- 1} & {- 1} & {- 1} \\ 1 & 1 & {- 1} & {- 1} \\ {- 1} & 1 & 1 & {- 1} \\ 1 & {- 1} & {- 1} & 1 \\ {- 1} & {- 1} & 1 & 1 \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ {- 1} & 1 & {- 1} & 1 \\ 1 & {- 1} & 1 & {- 1} \\ {- 1} & {- 1} & {- 1} & {- 1} \\ j & j & {- j} & {- j} \\ {- j} & j & j & {- j} \\ j & {- j} & {- j} & j \\ {- j} & {- j} & j & j \end{bmatrix}\]

12 – 15

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ {- 1} & 1 & {- 1} & 1 \\ {- 1} & 1 & {- 1} & 1 \\ 1 & 1 & {- 1} & {- 1} \\ 1 & 1 & {- 1} & {- 1} \\ {- 1} & 1 & 1 & {- 1} \\ {- 1} & 1 & 1 & {- 1} \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ {- 1} & 1 & {- 1} & 1 \\ {- 1} & 1 & {- 1} & 1 \\ j & j & {- j} & {- j} \\ j & j & {- j} & {- j} \\ {- j} & j & j & {- j} \\ {- j} & j & j & {- j} \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & {- 1} & 1 & {- 1} \\ {- 1} & {- 1} & {- 1} & {- 1} \\ {- 1} & 1 & {- 1} & 1 \\ 1 & 1 & {- 1} & {- 1} \\ 1 & {- 1} & {- 1} & 1 \\ {- 1} & {- 1} & 1 & 1 \\ {- 1} & 1 & 1 & {- 1} \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & {- 1} & 1 & {- 1} \\ {- 1} & {- 1} & {- 1} & {- 1} \\ {- 1} & 1 & {- 1} & 1 \\ j & j & {- j} & {- j} \\ j & {- j} & {- j} & j \\ {- j} & {- j} & j & j \\ {- j} & j & j & {- j} \end{bmatrix}\]

16 – 19

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & {- 1} & 1 & {- 1} \\ {- 1} & 1 & {- 1} & 1 \\ {- 1} & {- 1} & {- 1} & {- 1} \\ 1 & 1 & {- 1} & {- 1} \\ 1 & {- 1} & {- 1} & 1 \\ {- 1} & 1 & 1 & {- 1} \\ {- 1} & {- 1} & 1 & 1 \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & {- 1} & 1 & {- 1} \\ {- 1} & 1 & {- 1} & 1 \\ {- 1} & {- 1} & {- 1} & {- 1} \\ j & j & {- j} & {- j} \\ j & {- j} & {- j} & j \\ {- j} & j & j & {- j} \\ {- j} & {- j} & j & j \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & {- 1} & {- 1} \\ {- 1} & 1 & {- 1} & 1 \\ 1 & {- 1} & 1 & {- 1} \\ 1 & 1 & {- 1} & {- 1} \\ {- 1} & {- 1} & 1 & 1 \\ {- 1} & 1 & 1 & {- 1} \\ 1 & {- 1} & {- 1} & 1 \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & {- 1} & {- 1} \\ {- 1} & 1 & {- 1} & 1 \\ 1 & {- 1} & 1 & {- 1} \\ j & j & {- j} & {- j} \\ {- j} & {- j} & j & j \\ {- j} & j & j & {- j} \\ j & {- j} & {- j} & j \end{bmatrix}\]

20 – 23

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ {- 1} & 1 & {- 1} & 1 \\ {- 1} & {- 1} & {- 1} & {- 1} \\ 1 & {- 1} & 1 & {- 1} \\ 1 & 1 & {- 1} & {- 1} \\ {- 1} & 1 & 1 & {- 1} \\ {- 1} & {- 1} & 1 & 1 \\ 1 & {- 1} & {- 1} & 1 \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ {- 1} & 1 & {- 1} & 1 \\ {- 1} & {- 1} & {- 1} & {- 1} \\ 1 & {- 1} & 1 & {- 1} \\ j & j & {- j} & {- j} \\ {- j} & j & j & {- j} \\ {- j} & {- j} & j & j \\ j & {- j} & {- j} & j \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ {- 1} & 1 & {- 1} & 1 \\ {- 1} & 1 & {- 1} & 1 \\ 1 & 1 & 1 & 1 \\ 1 & 1 & {- 1} & {- 1} \\ {- 1} & 1 & 1 & {- 1} \\ {- 1} & 1 & 1 & {- 1} \\ 1 & 1 & {- 1} & {- 1} \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ {- 1} & 1 & {- 1} & 1 \\ {- 1} & 1 & {- 1} & 1 \\ 1 & 1 & 1 & 1 \\ j & j & {- j} & {- j} \\ {- j} & j & j & {- j} \\ {- j} & j & j & {- j} \\ j & j & {- j} & {- j} \end{bmatrix}\]

 

Table 6.3.1.5-21: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook1=ng1n2n2 and five-layer transmission using eight antenna ports with transform precoding disabled.

TPMI index

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)(ordered from left to right in increasing order of TPMI index)

0 – 1

\[\frac{1}{2\sqrt[{}]{10}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & {- 1} \\ 1 & 1 & {- 1} & {- 1} & {- 1} \\ 1 & 1 & {- 1} & {- 1} & 1 \\ 1 & {- 1} & 1 & {- 1} & 1 \\ 1 & {- 1} & 1 & {- 1} & {- 1} \\ 1 & {- 1} & {- 1} & 1 & {- 1} \\ 1 & {- 1} & {- 1} & 1 & 1 \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{10}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & {- 1} \\ 1 & 1 & {- 1} & {- 1} & {- 1} \\ 1 & 1 & {- 1} & {- 1} & 1 \\ j & {- j} & 1 & {- 1} & 1 \\ j & {- j} & 1 & {- 1} & {- 1} \\ j & {- j} & {- 1} & 1 & {- 1} \\ j & {- j} & {- 1} & 1 & 1 \end{bmatrix}\]

2 – 3

\[\frac{1}{2\sqrt[{}]{10}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & {- 1} & {- 1} & 1 \\ 1 & 1 & {- 1} & {- 1} & {- 1} \\ {- 1} & {- 1} & 1 & 1 & {- 1} \\ 1 & {- 1} & 1 & {- 1} & 1 \\ {- 1} & 1 & {- 1} & 1 & 1 \\ 1 & {- 1} & {- 1} & 1 & {- 1} \\ {- 1} & 1 & 1 & {- 1} & {- 1} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{10}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & {- 1} & {- 1} & 1 \\ 1 & 1 & {- 1} & {- 1} & {- 1} \\ {- 1} & {- 1} & 1 & 1 & {- 1} \\ j & {- j} & 1 & {- 1} & 1 \\ {- j} & j & {- 1} & 1 & 1 \\ j & {- j} & {- 1} & 1 & {- 1} \\ {- j} & j & 1 & {- 1} & {- 1} \end{bmatrix}\]

4 – 5

\[\frac{1}{2\sqrt[{}]{10}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & {- 1} \\ {- 1} & {- 1} & 1 & 1 & 1 \\ {- 1} & {- 1} & 1 & 1 & {- 1} \\ 1 & {- 1} & 1 & {- 1} & 1 \\ 1 & {- 1} & 1 & {- 1} & {- 1} \\ {- 1} & 1 & 1 & {- 1} & 1 \\ {- 1} & 1 & 1 & {- 1} & {- 1} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{10}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & {- 1} \\ {- 1} & {- 1} & 1 & 1 & 1 \\ {- 1} & {- 1} & 1 & 1 & {- 1} \\ j & {- j} & 1 & {- 1} & 1 \\ j & {- j} & 1 & {- 1} & {- 1} \\ {- j} & j & 1 & {- 1} & 1 \\ {- j} & j & 1 & {- 1} & {- 1} \end{bmatrix}\]

6 – 7

\[\frac{1}{2\sqrt[{}]{10}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & {- 1} & {- 1} & 1 \\ {- 1} & {- 1} & 1 & 1 & 1 \\ 1 & 1 & {- 1} & {- 1} & 1 \\ 1 & {- 1} & 1 & {- 1} & 1 \\ {- 1} & 1 & {- 1} & 1 & 1 \\ {- 1} & 1 & 1 & {- 1} & 1 \\ 1 & {- 1} & {- 1} & 1 & 1 \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{10}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & {- 1} & {- 1} & 1 \\ {- 1} & {- 1} & 1 & 1 & 1 \\ 1 & 1 & {- 1} & {- 1} & 1 \\ j & {- j} & 1 & {- 1} & 1 \\ {- j} & j & {- 1} & 1 & 1 \\ {- j} & j & 1 & {- 1} & 1 \\ j & {- j} & {- 1} & 1 & 1 \end{bmatrix}\]

 

Table 6.3.1.5-22: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook1=ng1n2n2 and six-layer transmission using eight antenna ports with transform precoding disabled.

TPMI index

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)(ordered from left to right in increasing order of TPMI index)

0 – 1

\[\frac{1}{4\sqrt[{}]{3}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & {- 1} & {- 1} \\ 1 & 1 & {- 1} & {- 1} & {- 1} & {- 1} \\ 1 & 1 & {- 1} & {- 1} & 1 & 1 \\ 1 & {- 1} & 1 & {- 1} & 1 & {- 1} \\ 1 & {- 1} & 1 & {- 1} & {- 1} & 1 \\ 1 & {- 1} & {- 1} & 1 & {- 1} & 1 \\ 1 & {- 1} & {- 1} & 1 & 1 & {- 1} \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{3}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & {- 1} & {- 1} \\ 1 & 1 & {- 1} & {- 1} & {- 1} & {- 1} \\ 1 & 1 & {- 1} & {- 1} & 1 & 1 \\ j & {- j} & j & {- j} & 1 & {- 1} \\ j & {- j} & j & {- j} & {- 1} & 1 \\ j & {- j} & {- j} & j & {- 1} & 1 \\ j & {- j} & {- j} & j & 1 & {- 1} \end{bmatrix}\]

2 – 3

\[\frac{1}{4\sqrt[{}]{3}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & {- 1} & {- 1} & 1 & 1 \\ 1 & 1 & {- 1} & {- 1} & {- 1} & {- 1} \\ {- 1} & {- 1} & 1 & 1 & {- 1} & {- 1} \\ 1 & {- 1} & 1 & {- 1} & 1 & {- 1} \\ {- 1} & 1 & {- 1} & 1 & 1 & {- 1} \\ 1 & {- 1} & {- 1} & 1 & {- 1} & 1 \\ {- 1} & 1 & 1 & {- 1} & {- 1} & 1 \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{3}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & {- 1} & {- 1} & 1 & 1 \\ 1 & 1 & {- 1} & {- 1} & {- 1} & {- 1} \\ {- 1} & {- 1} & 1 & 1 & {- 1} & {- 1} \\ j & {- j} & j & {- j} & 1 & {- 1} \\ {- j} & j & {- j} & j & 1 & {- 1} \\ j & {- j} & {- j} & j & {- 1} & 1 \\ {- j} & j & j & {- j} & {- 1} & 1 \end{bmatrix}\]

4 – 5

\[\frac{1}{4\sqrt[{}]{3}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & {- 1} & {- 1} \\ {- 1} & {- 1} & 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & 1 & 1 & {- 1} & {- 1} \\ 1 & {- 1} & 1 & {- 1} & 1 & {- 1} \\ 1 & {- 1} & 1 & {- 1} & {- 1} & 1 \\ {- 1} & 1 & 1 & {- 1} & 1 & {- 1} \\ {- 1} & 1 & 1 & {- 1} & {- 1} & 1 \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{3}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & {- 1} & {- 1} \\ {- 1} & {- 1} & 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & 1 & 1 & {- 1} & {- 1} \\ j & {- j} & j & {- j} & 1 & {- 1} \\ j & {- j} & j & {- j} & {- 1} & 1 \\ {- j} & j & j & {- j} & 1 & {- 1} \\ {- j} & j & j & {- j} & {- 1} & 1 \end{bmatrix}\]

6 – 7

\[\frac{1}{4\sqrt[{}]{3}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & {- 1} & {- 1} & 1 & 1 \\ {- 1} & {- 1} & 1 & 1 & 1 & 1 \\ 1 & 1 & {- 1} & {- 1} & 1 & 1 \\ 1 & {- 1} & 1 & {- 1} & 1 & {- 1} \\ {- 1} & 1 & {- 1} & 1 & 1 & {- 1} \\ {- 1} & 1 & 1 & {- 1} & 1 & {- 1} \\ 1 & {- 1} & {- 1} & 1 & 1 & {- 1} \end{bmatrix}\]

\[\frac{1}{4\sqrt[{}]{3}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & {- 1} & {- 1} & 1 & 1 \\ {- 1} & {- 1} & 1 & 1 & 1 & 1 \\ 1 & 1 & {- 1} & {- 1} & 1 & 1 \\ j & {- j} & j & {- j} & 1 & {- 1} \\ {- j} & j & {- j} & j & 1 & {- 1} \\ {- j} & j & j & {- j} & 1 & {- 1} \\ j & {- j} & {- j} & j & 1 & {- 1} \end{bmatrix}\]

 

Table 6.3.1.5-23: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook1=ng1n2n2 and seven-layer transmission using eight antenna ports with transform precoding disabled.

TPMI index

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)(ordered from left to right in increasing order of TPMI index)

0 – 1

\[\frac{1}{2\sqrt[{}]{14}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & {- 1} & {- 1} & {- 1} & {- 1} \\ 1 & 1 & {- 1} & 1 & 1 & {- 1} & {- 1} \\ 1 & 1 & {- 1} & {- 1} & {- 1} & 1 & 1 \\ 1 & {- 1} & 1 & 1 & {- 1} & 1 & {- 1} \\ 1 & {- 1} & 1 & {- 1} & 1 & {- 1} & 1 \\ 1 & {- 1} & {- 1} & 1 & {- 1} & {- 1} & 1 \\ 1 & {- 1} & {- 1} & {- 1} & 1 & 1 & {- 1} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{14}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & {- 1} & {- 1} & {- 1} & {- 1} \\ 1 & 1 & {- 1} & 1 & 1 & {- 1} & {- 1} \\ 1 & 1 & {- 1} & {- 1} & {- 1} & 1 & 1 \\ j & {- j} & j & 1 & {- 1} & 1 & {- 1} \\ j & {- j} & j & {- 1} & 1 & {- 1} & 1 \\ j & {- j} & {- j} & 1 & {- 1} & {- 1} & 1 \\ j & {- j} & {- j} & {- 1} & 1 & 1 & {- 1} \end{bmatrix}\]

2 – 3

\[\frac{1}{2\sqrt[{}]{14}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & {- 1} & 1 & 1 & 1 & 1 \\ 1 & 1 & {- 1} & 1 & 1 & {- 1} & {- 1} \\ {- 1} & {- 1} & 1 & 1 & 1 & {- 1} & {- 1} \\ 1 & {- 1} & 1 & 1 & {- 1} & 1 & {- 1} \\ {- 1} & 1 & {- 1} & 1 & {- 1} & 1 & {- 1} \\ 1 & {- 1} & {- 1} & 1 & {- 1} & {- 1} & 1 \\ {- 1} & 1 & 1 & 1 & {- 1} & {- 1} & 1 \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{14}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & {- 1} & 1 & 1 & 1 & 1 \\ 1 & 1 & {- 1} & 1 & 1 & {- 1} & {- 1} \\ {- 1} & {- 1} & 1 & 1 & 1 & {- 1} & {- 1} \\ j & {- j} & j & 1 & {- 1} & 1 & {- 1} \\ {- j} & j & {- j} & 1 & {- 1} & 1 & {- 1} \\ j & {- j} & {- j} & 1 & {- 1} & {- 1} & 1 \\ {- j} & j & j & 1 & {- 1} & {- 1} & 1 \end{bmatrix}\]

4 – 5

\[\frac{1}{2\sqrt[{}]{14}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & {- 1} & {- 1} & {- 1} & {- 1} \\ {- 1} & {- 1} & 1 & {- 1} & {- 1} & 1 & 1 \\ {- 1} & {- 1} & 1 & 1 & 1 & {- 1} & {- 1} \\ 1 & {- 1} & 1 & 1 & {- 1} & 1 & {- 1} \\ 1 & {- 1} & 1 & {- 1} & 1 & {- 1} & 1 \\ {- 1} & 1 & 1 & {- 1} & 1 & 1 & {- 1} \\ {- 1} & 1 & 1 & 1 & {- 1} & {- 1} & 1 \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{14}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & {- 1} & {- 1} & {- 1} & {- 1} \\ {- 1} & {- 1} & 1 & {- 1} & {- 1} & 1 & 1 \\ {- 1} & {- 1} & 1 & 1 & 1 & {- 1} & {- 1} \\ j & {- j} & j & 1 & {- 1} & 1 & {- 1} \\ j & {- j} & j & {- 1} & 1 & {- 1} & 1 \\ {- j} & j & j & {- 1} & 1 & 1 & {- 1} \\ {- j} & j & j & 1 & {- 1} & {- 1} & 1 \end{bmatrix}\]

6 – 7

\[\frac{1}{2\sqrt[{}]{14}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & {- 1} & 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & 1 & {- 1} & {- 1} & 1 & 1 \\ 1 & 1 & {- 1} & {- 1} & {- 1} & 1 & 1 \\ 1 & {- 1} & 1 & 1 & {- 1} & 1 & {- 1} \\ {- 1} & 1 & {- 1} & 1 & {- 1} & 1 & {- 1} \\ {- 1} & 1 & 1 & {- 1} & 1 & 1 & {- 1} \\ 1 & {- 1} & {- 1} & {- 1} & 1 & 1 & {- 1} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{14}}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & {- 1} & 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & 1 & {- 1} & {- 1} & 1 & 1 \\ 1 & 1 & {- 1} & {- 1} & {- 1} & 1 & 1 \\ j & {- j} & j & 1 & {- 1} & 1 & {- 1} \\ {- j} & j & {- j} & 1 & {- 1} & 1 & {- 1} \\ {- j} & j & j & {- 1} & 1 & 1 & {- 1} \\ j & {- j} & {- j} & {- 1} & 1 & 1 & {- 1} \end{bmatrix}\]

 

Table 6.3.1.5-24: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook1=ng1n2n2 and eight-layer transmission using eight antenna ports with transform precoding disabled.

TPMI index

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)(ordered from left to right in increasing order of TPMI index)

0 – 1

\[\frac{1}{8}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & {- 1} & {- 1} & {- 1} & {- 1} \\ 1 & 1 & {- 1} & {- 1} & 1 & 1 & {- 1} & {- 1} \\ 1 & 1 & {- 1} & {- 1} & {- 1} & {- 1} & 1 & 1 \\ 1 & {- 1} & 1 & {- 1} & 1 & {- 1} & 1 & {- 1} \\ 1 & {- 1} & 1 & {- 1} & {- 1} & 1 & {- 1} & 1 \\ 1 & {- 1} & {- 1} & 1 & 1 & {- 1} & {- 1} & 1 \\ 1 & {- 1} & {- 1} & 1 & {- 1} & 1 & 1 & {- 1} \end{bmatrix}\]

\[\frac{1}{8}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & {- 1} & {- 1} & {- 1} & {- 1} \\ 1 & 1 & {- 1} & {- 1} & 1 & 1 & {- 1} & {- 1} \\ 1 & 1 & {- 1} & {- 1} & {- 1} & {- 1} & 1 & 1 \\ j & {- j} & j & {- j} & 1 & {- 1} & 1 & {- 1} \\ j & {- j} & j & {- j} & {- 1} & 1 & {- 1} & 1 \\ j & {- j} & {- j} & j & 1 & {- 1} & {- 1} & 1 \\ j & {- j} & {- j} & j & {- 1} & 1 & 1 & {- 1} \end{bmatrix}\]

2 – 3

\[\frac{1}{8}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & {- 1} & {- 1} & 1 & 1 & 1 & 1 \\ 1 & 1 & {- 1} & {- 1} & 1 & 1 & {- 1} & {- 1} \\ {- 1} & {- 1} & 1 & 1 & 1 & 1 & {- 1} & {- 1} \\ 1 & {- 1} & 1 & {- 1} & 1 & {- 1} & 1 & {- 1} \\ {- 1} & 1 & {- 1} & 1 & 1 & {- 1} & 1 & {- 1} \\ 1 & {- 1} & {- 1} & 1 & 1 & {- 1} & {- 1} & 1 \\ {- 1} & 1 & 1 & {- 1} & 1 & {- 1} & {- 1} & 1 \end{bmatrix}\]

\[\frac{1}{8}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & {- 1} & {- 1} & 1 & 1 & 1 & 1 \\ 1 & 1 & {- 1} & {- 1} & 1 & 1 & {- 1} & {- 1} \\ {- 1} & {- 1} & 1 & 1 & 1 & 1 & {- 1} & {- 1} \\ j & {- j} & j & {- j} & 1 & {- 1} & 1 & {- 1} \\ {- j} & j & {- j} & j & 1 & {- 1} & 1 & {- 1} \\ j & {- j} & {- j} & j & 1 & {- 1} & {- 1} & 1 \\ {- j} & j & j & {- j} & 1 & {- 1} & {- 1} & 1 \end{bmatrix}\]

4 – 5

\[\frac{1}{8}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & {- 1} & {- 1} & {- 1} & {- 1} \\ {- 1} & {- 1} & 1 & 1 & {- 1} & {- 1} & 1 & 1 \\ {- 1} & {- 1} & 1 & 1 & 1 & 1 & {- 1} & {- 1} \\ 1 & {- 1} & 1 & {- 1} & 1 & {- 1} & 1 & {- 1} \\ 1 & {- 1} & 1 & {- 1} & {- 1} & 1 & {- 1} & 1 \\ {- 1} & 1 & 1 & {- 1} & {- 1} & 1 & 1 & {- 1} \\ {- 1} & 1 & 1 & {- 1} & 1 & {- 1} & {- 1} & 1 \end{bmatrix}\]

\[\frac{1}{8}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & {- 1} & {- 1} & {- 1} & {- 1} \\ {- 1} & {- 1} & 1 & 1 & {- 1} & {- 1} & 1 & 1 \\ {- 1} & {- 1} & 1 & 1 & 1 & 1 & {- 1} & {- 1} \\ j & {- j} & j & {- j} & 1 & {- 1} & 1 & {- 1} \\ j & {- j} & j & {- j} & {- 1} & 1 & {- 1} & 1 \\ {- j} & j & j & {- j} & {- 1} & 1 & 1 & {- 1} \\ {- j} & j & j & {- j} & 1 & {- 1} & {- 1} & 1 \end{bmatrix}\]

6 – 7

\[\frac{1}{8}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & {- 1} & {- 1} & 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & 1 & 1 & {- 1} & {- 1} & 1 & 1 \\ 1 & 1 & {- 1} & {- 1} & {- 1} & {- 1} & 1 & 1 \\ 1 & {- 1} & 1 & {- 1} & 1 & {- 1} & 1 & {- 1} \\ {- 1} & 1 & {- 1} & 1 & 1 & {- 1} & 1 & {- 1} \\ {- 1} & 1 & 1 & {- 1} & {- 1} & 1 & 1 & {- 1} \\ 1 & {- 1} & {- 1} & 1 & {- 1} & 1 & 1 & {- 1} \end{bmatrix}\]

\[\frac{1}{8}\begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & {- 1} & {- 1} & 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & 1 & 1 & {- 1} & {- 1} & 1 & 1 \\ 1 & 1 & {- 1} & {- 1} & {- 1} & {- 1} & 1 & 1 \\ j & {- j} & j & {- j} & 1 & {- 1} & 1 & {- 1} \\ {- j} & j & {- j} & j & 1 & {- 1} & 1 & {- 1} \\ {- j} & j & j & {- j} & {- 1} & 1 & 1 & {- 1} \\ j & {- j} & {- j} & j & {- 1} & 1 & 1 & {- 1} \end{bmatrix}\]

 

Table 6.3.1.5-25: Submatrices \({\bar{\mathbf{W}}}_{1,\mathbf{i}}\) for codebook2 and used in Tables 6.3.1.5-29 to 6.3.1.5-31.

\[\mathbf{i}\]

\[\begin{matrix} {{\bar{\mathbf{W}}}_{1,\mathbf{i}}} \end{matrix}\]

0 – 7

\[\frac{1}{2}\begin{bmatrix} 1 \\ 1 \\ 1 \\ 1 \end{bmatrix}\]

\[\frac{1}{2}\begin{bmatrix} 1 \\ 1 \\ j \\ j \end{bmatrix}\]

\[\frac{1}{2}\begin{bmatrix} 1 \\ 1 \\ {- 1} \\ {- 1} \end{bmatrix}\]

\[\frac{1}{2}\begin{bmatrix} 1 \\ 1 \\ {- j} \\ {- j} \end{bmatrix}\]

\[\frac{1}{2}\begin{bmatrix} 1 \\ j \\ 1 \\ j \end{bmatrix}\]

\[\frac{1}{2}\begin{bmatrix} 1 \\ j \\ j \\ {- 1} \end{bmatrix}\]

\[\frac{1}{2}\begin{bmatrix} 1 \\ j \\ {- 1} \\ {- j} \end{bmatrix}\]

\[\frac{1}{2}\begin{bmatrix} 1 \\ j \\ {- j} \\ 1 \end{bmatrix}\]

8 – 15

\[\frac{1}{2}\begin{bmatrix} 1 \\ {- 1} \\ 1 \\ {- 1} \end{bmatrix}\]

\[\frac{1}{2}\begin{bmatrix} 1 \\ {- 1} \\ j \\ {- j} \end{bmatrix}\]

\[\frac{1}{2}\begin{bmatrix} 1 \\ {- 1} \\ {- 1} \\ 1 \end{bmatrix}\]

\[\frac{1}{2}\begin{bmatrix} 1 \\ {- 1} \\ {- j} \\ j \end{bmatrix}\]

\[\frac{1}{2}\begin{bmatrix} 1 \\ {- j} \\ 1 \\ {- j} \end{bmatrix}\]

\[\frac{1}{2}\begin{bmatrix} 1 \\ {- j} \\ j \\ 1 \end{bmatrix}\]

\[\frac{1}{2}\begin{bmatrix} 1 \\ {- j} \\ {- 1} \\ j \end{bmatrix}\]

\[\frac{1}{2}\begin{bmatrix} 1 \\ {- j} \\ {- j} \\ {- 1} \end{bmatrix}\]

 

Table 6.3.1.5-26: Submatrices \({\bar{\mathbf{W}}}_{2,\mathbf{i}}\) for codebook2 and used in Tables 6.3.1.5-30 to 6.3.1.5-33.

\[\mathbf{i}\]

\[\begin{matrix} {{\bar{\mathbf{W}}}_{2,\mathbf{i}}} \end{matrix}\]

0 – 3

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 \\ 1 & 1 \\ 1 & {- 1} \\ 1 & {- 1} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 \\ 1 & 1 \\ j & {- j} \\ j & {- j} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 \\ j & j \\ 1 & {- 1} \\ j & {- j} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 \\ j & j \\ j & {- j} \\ {- 1} & 1 \end{bmatrix}\]

4 – 7

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 \\ {- 1} & {- 1} \\ 1 & {- 1} \\ {- 1} & 1 \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 \\ {- 1} & {- 1} \\ j & {- j} \\ {- j} & j \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 \\ {- j} & {- j} \\ 1 & {- 1} \\ {- j} & j \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 & 1 \\ {- j} & {- j} \\ j & {- j} \\ 1 & {- 1} \end{bmatrix}\]

 

Table 6.3.1.5-27: Submatrices \({\bar{\mathbf{W}}}_{3,\mathbf{i}}\) for codebook2 and used in Tables 6.3.1.5-31, 6.3.1.5-33, 6.3.1.5-34, and 6.3.1.5-35.

\[\mathbf{i}\]

\[\begin{matrix} {{\bar{\mathbf{W}}}_{3,\mathbf{i}}} \end{matrix}\]

0 – 3

\[\frac{1}{2\sqrt[{}]{3}}\begin{bmatrix} 1 & 1 & 1 \\ 1 & {- 1} & 1 \\ 1 & 1 & {- 1} \\ 1 & {- 1} & {- 1} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{3}}\begin{bmatrix} 1 & 1 & 1 \\ 1 & {- 1} & 1 \\ j & j & {- j} \\ j & {- j} & {- j} \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{3}}\begin{bmatrix} 1 & 1 & 1 \\ {- 1} & 1 & {- 1} \\ 1 & 1 & {- 1} \\ {- 1} & 1 & 1 \end{bmatrix}\]

\[\frac{1}{2\sqrt[{}]{3}}\begin{bmatrix} 1 & 1 & 1 \\ {- 1} & 1 & {- 1} \\ j & j & {- j} \\ {- j} & j & j \end{bmatrix}\]

 

Table 6.3.1.5-28: Submatrices \({\bar{\mathbf{W}}}_{4,\mathbf{i}}\) for codebook2 and used in Tables 6.3.1.5-32, 6.3.1.5-35, and 6.3.1.5-36.

\[\mathbf{i}\]

\[\begin{matrix} {{\bar{\mathbf{W}}}_{4,\mathbf{i}}} \end{matrix}\]

0 – 1

\[\frac{1}{4}\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & {- 1} & 1 & {- 1} \\ 1 & 1 & {- 1} & {- 1} \\ 1 & {- 1} & {- 1} & 1 \end{bmatrix}\]

\[\frac{1}{4}\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & {- 1} & 1 & {- 1} \\ j & j & {- j} & {- j} \\ j & {- j} & {- j} & j \end{bmatrix}\]

 

Table 6.3.1.5-29: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook2 and single-layer transmission using eight antenna ports.

TPMI index \(\mathbf{i}\)

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)

0 – 15

\[\frac{1}{\sqrt[{}]{2}}\begin{bmatrix} {\bar{W}}_{1,i} \\ 0_{4 \times 1} \end{bmatrix}\]

16 – 31

\[\frac{1}{\sqrt[{}]{2}}\begin{bmatrix} 0_{4 \times 1} \\ {\bar{W}}_{1,(i - 16)} \end{bmatrix}\]

32

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} 1 \\ 1 \end{matrix} \\ 1 \\ 1 \end{matrix} \\ 1 \end{matrix} \\ 1 \\ 1 \end{matrix} \\ 1 \end{bmatrix}\]

 

Table 6.3.1.5-30: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook2 and two-layer transmission using eight antenna ports with transform precoding disabled.

TPMI index \(\mathbf{i}\)

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)

0 – 7

\[\frac{1}{\sqrt[{}]{2}}\begin{bmatrix} {\bar{W}}_{2,i} \\ 0_{4 \times 2} \end{bmatrix}\]

8 – 15

\[\frac{1}{\sqrt[{}]{2}}\begin{bmatrix} 0_{4 \times 2} \\ {\bar{W}}_{2,{({i - 8})}} \end{bmatrix}\]

16 – 271

\[\frac{1}{\sqrt[{}]{2}}\begin{bmatrix} {\bar{W}}_{1,{\lfloor{{(i - 16)}/16}\rfloor}} & 0_{4 \times 1} \\ 0_{4 \times 1} & {\bar{W}}_{1,{({imod16})}} \end{bmatrix}\]

 

Table 6.3.1.5-31: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook2 and three-layer transmission using eight antenna ports with transform precoding disabled.

TPMI index \(\mathbf{i}\)

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)

0 – 3

\[\frac{1}{\sqrt[{}]{2}}\begin{bmatrix} {\bar{W}}_{3,i} \\ 0_{4 \times 3} \end{bmatrix}\]

4 – 7

\[\frac{1}{\sqrt[{}]{2}}\begin{bmatrix} 0_{4 \times 3} \\ {\bar{W}}_{3,{({i - 4})}} \end{bmatrix}\]

8 – 135

\[\frac{1}{\sqrt[{}]{2}}\begin{bmatrix} {\bar{W}}_{1,{\lfloor{{(i - 8)}/8}\rfloor}} & 0_{4 \times 2} \\ 0_{4 \times 1} & {\bar{W}}_{2,{({imod8})}} \end{bmatrix}\]

136 – 263

\[\frac{1}{\sqrt[{}]{2}}\begin{bmatrix} {\bar{W}}_{2,{\lfloor{{(i - 136)}/16}\rfloor}} & 0_{4 \times 1} \\ 0_{4 \times 2} & {\bar{W}}_{1,{({{({i - 136})}mod16})}} \end{bmatrix}\]

 

Table 6.3.1.5-32: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook2 and four-layer transmission using eight antenna ports with transform precoding disabled.

TPMI index \(\mathbf{i}\)

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)

0 – 1

\[\frac{1}{\sqrt[{}]{2}}\begin{bmatrix} {\bar{W}}_{4,i} \\ 0_{4 \times 4} \end{bmatrix}\]

2 – 3

\[\frac{1}{\sqrt[{}]{2}}\begin{bmatrix} 0_{4 \times 4} \\ {\bar{W}}_{4,{({i - 2})}} \end{bmatrix}\]

4 – 67

\[\frac{1}{\sqrt[{}]{2}}\begin{bmatrix} {\bar{W}}_{2,{\lfloor{{(i - 4)}/8}\rfloor}} & 0_{4 \times 2} \\ 0_{4 \times 2} & {\bar{W}}_{2,{({{({i - 4})}mod8})}} \end{bmatrix}\]

 

Table 6.3.1.5-33: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook2 and five-layer transmission using eight antenna ports with transform precoding disabled.

TPMI index \(\mathbf{i}\)

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)

0 – 31

\[\frac{1}{\sqrt[{}]{2}}\begin{bmatrix} {\bar{W}}_{2,{\lfloor{i/4}\rfloor}} & 0_{4 \times 3} \\ 0_{4 \times 2} & {\bar{W}}_{3,(imod4)} \end{bmatrix}\]

 

Table 6.3.1.5-34: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook2 and six-layer transmission using eight antenna ports with transform precoding disabled.

TPMI index \(\mathbf{i}\)

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)

0 – 15

\[\frac{1}{\sqrt[{}]{2}}\begin{bmatrix} {\bar{W}}_{3,{\lfloor{i/4}\rfloor}} & 0_{4 \times 3} \\ 0_{4 \times 3} & {\bar{W}}_{3,(imod4)} \end{bmatrix}\]

 

Table 6.3.1.5-35: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook2 and seven-layer transmission using eight antenna ports with transform precoding disabled.

TPMI index \(\mathbf{i}\)

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)

0 – 7

\[\frac{1}{\sqrt[{}]{2}}\begin{bmatrix} {\bar{W}}_{3,{\lfloor{i/2}\rfloor}} & 0_{4 \times 4} \\ 0_{4 \times 3} & {\bar{W}}_{4,(imod2)} \end{bmatrix}\]

 

Table 6.3.1.5-36: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook2 and eight-layer transmission using eight antenna ports with transform precoding disabled.

TPMI index \(\mathbf{i}\)

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)

0 – 3

\[\frac{1}{\sqrt[{}]{2}}\begin{bmatrix} {\bar{W}}_{4,{\lfloor{i/2}\rfloor}} & 0_{4 \times 4} \\ 0_{4 \times 4} & {\bar{W}}_{4,(imod2)} \end{bmatrix}\]

 

Table 6.3.1.5-37: Submatrices \({\bar{\mathbf{W}}}_{1,\mathbf{i}}\) for codebook3 and used in Tables 6.3.1.5-39 to 6.3.1.5-45.

\[\mathbf{i}\]

\[\begin{matrix} {{\bar{\mathbf{W}}}_{1,\mathbf{i}}} \end{matrix}\]

0 – 3

\[\frac{1}{\sqrt[{}]{2}}\begin{bmatrix} 1 \\ 1 \end{bmatrix}\]

\[\frac{1}{\sqrt[{}]{2}}\begin{bmatrix} 1 \\ {- 1} \end{bmatrix}\]

\[\frac{1}{\sqrt[{}]{2}}\begin{bmatrix} 1 \\ j \end{bmatrix}\]

\[\frac{1}{\sqrt[{}]{2}}\begin{bmatrix} 1 \\ {- j} \end{bmatrix}\]

 

Table 6.3.1.5-38: Submatrices \({\bar{\mathbf{W}}}_{2,\mathbf{i}}\) for codebook3 and used in Tables 6.3.1.5-40 to 6.3.1.5-46.

\[\mathbf{i}\]

\[\begin{matrix} {{\bar{\mathbf{W}}}_{2,\mathbf{i}}} \end{matrix}\]

0 – 1

\[\frac{1}{2}\left\lbrack {\begin{matrix} 1 \\ 1 \end{matrix}\begin{matrix} 1 \\ {- 1} \end{matrix}} \right\rbrack\]

\[\frac{1}{2}\left\lbrack {\begin{matrix} 1 \\ j \end{matrix}\begin{matrix} 1 \\ {- j} \end{matrix}} \right\rbrack\]

 

Table 6.3.1.5-39: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook3 and single-layer transmission using eight antenna ports.

TPMI index \(\mathbf{i}\)

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)

0 – 3

\[\frac{1}{2}\begin{bmatrix} {\bar{W}}_{1,i} \\ 0_{2 \times 1} \\ 0_{2 \times 1} \\ 0_{2 \times 1} \end{bmatrix}\]

4 – 7

\[\frac{1}{2}\begin{bmatrix} 0_{2 \times 1} \\ {\bar{W}}_{1,(i - 4)} \\ 0_{2 \times 1} \\ 0_{2 \times 1} \end{bmatrix}\]

8 – 11

\[\frac{1}{2}\begin{bmatrix} 0_{2 \times 1} \\ 0_{2 \times 1} \\ {\bar{W}}_{1,(i - 8)} \\ 0_{2 \times 1} \end{bmatrix}\]

12 – 15

\[\frac{1}{2}\begin{bmatrix} 0_{2 \times 1} \\ 0_{2 \times 1} \\ 0_{2 \times 1} \\ {\bar{W}}_{1,(i - 12)} \end{bmatrix}\]

16

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} 1 \\ 1 \end{matrix} \\ 1 \\ 1 \end{matrix} \\ 1 \end{matrix} \\ 1 \\ 1 \end{matrix} \\ 1 \end{bmatrix}\]

 

Table 6.3.1.5-40: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook3 and two-layer transmission using eight antenna ports with transform precoding disabled.

TPMI index \(\mathbf{i}\)

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)

0 – 1

\[\frac{1}{2}\begin{bmatrix} {\bar{W}}_{2,i} \\ 0_{2 \times 2} \\ 0_{2 \times 2} \\ 0_{2 \times 2} \end{bmatrix}\]

2 – 3

\[\frac{1}{2}\begin{bmatrix} 0_{2 \times 2} \\ {\bar{W}}_{2,(i - 2)} \\ 0_{2 \times 2} \\ 0_{2 \times 2} \end{bmatrix}\]

4 – 5

\[\frac{1}{2}\begin{bmatrix} 0_{2 \times 2} \\ 0_{2 \times 2} \\ {\bar{W}}_{2,(i - 4)} \\ 0_{2 \times 2} \end{bmatrix}\]

6 – 7

\[\frac{1}{2}\begin{bmatrix} 0_{2 \times 2} \\ 0_{2 \times 2} \\ 0_{2 \times 2} \\ {\bar{W}}_{2,(i - 6)} \end{bmatrix}\]

8 – 23

\[\frac{1}{2}\begin{bmatrix} {\bar{W}}_{1,{\lfloor{{(i - 8)}/4}\rfloor}} & 0_{2 \times 1} \\ 0_{2 \times 1} & {\bar{W}}_{1,{({imod4})}} \\ 0_{2 \times 1} & 0_{2 \times 1} \\ 0_{2 \times 1} & 0_{2 \times 1} \end{bmatrix}\]

24 – 39

\[\frac{1}{2}\begin{bmatrix} {\bar{W}}_{1,{\lfloor{{(i - 24)}/4}\rfloor}} & 0_{2 \times 1} \\ 0_{2 \times 1} & 0_{2 \times 1} \\ 0_{2 \times 1} & {\bar{W}}_{1,{({imod4})}} \\ 0_{2 \times 1} & 0_{2 \times 1} \end{bmatrix}\]

40 – 55

\[\frac{1}{2}\begin{bmatrix} {\bar{W}}_{1,{\lfloor{{(i - 40)}/4}\rfloor}} & 0_{2 \times 1} \\ 0_{2 \times 1} & 0_{2 \times 1} \\ 0_{2 \times 1} & 0_{2 \times 1} \\ 0_{2 \times 1} & {\bar{W}}_{1,{({imod4})}} \end{bmatrix}\]

56 – 71

\[\frac{1}{2}\begin{bmatrix} 0_{2 \times 1} & 0_{2 \times 1} \\ {\bar{W}}_{1,{\lfloor{{(i - 56)}/4}\rfloor}} & 0_{2 \times 1} \\ 0_{2 \times 1} & {\bar{W}}_{1,{({imod4})}} \\ 0_{2 \times 1} & 0_{2 \times 1} \end{bmatrix}\]

72 – 87

\[\frac{1}{2}\begin{bmatrix} 0_{2 \times 1} & 0_{2 \times 1} \\ {\bar{W}}_{1,{\lfloor{{(i - 72)}/4}\rfloor}} & 0_{2 \times 1} \\ 0_{2 \times 1} & 0_{2 \times 1} \\ 0_{2 \times 1} & {\bar{W}}_{1,{({imod4})}} \end{bmatrix}\]

88 – 103

\[\frac{1}{2}\begin{bmatrix} 0_{2 \times 1} & 0_{2 \times 1} \\ 0_{2 \times 1} & 0_{2 \times 1} \\ {\bar{W}}_{1,{\lfloor{{(i - 88)}/4}\rfloor}} & 0_{2 \times 1} \\ 0_{2 \times 1} & {\bar{W}}_{1,{({imod4})}} \end{bmatrix}\]

104

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} 1 \\ 1 \end{matrix} \\ 1 \\ 1 \end{matrix} \\ 0 \end{matrix} \\ 0 \\ 0 \end{matrix} \\ 0 \end{matrix} & \begin{matrix} 0 \\ 0 \\ \begin{matrix} 0 \\ 0 \\ \begin{matrix} 1 \\ 1 \\ \begin{matrix} 1 \\ 1 \end{matrix} \end{matrix} \end{matrix} \end{matrix} \end{bmatrix}\]

 

Table 6.3.1.5-41: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook3 and three-layer transmission using eight antenna ports with transform precoding disabled.

TPMI index \(\mathbf{i}\)

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)

0 – 7

\[\frac{1}{2}\begin{bmatrix} {\bar{W}}_{2,{\lfloor{i/4}\rfloor}} & 0_{2 \times 1} \\ 0_{2 \times 2} & {\bar{W}}_{1,{({imod4})}} \\ 0_{2 \times 2} & 0_{2 \times 1} \\ 0_{2 \times 2} & 0_{2 \times 1} \end{bmatrix}\]

8 – 15

\[\frac{1}{2}\begin{bmatrix} {\bar{W}}_{2,{\lfloor{{(i - 8)}/4}\rfloor}} & 0_{2 \times 1} \\ 0_{2 \times 2} & 0_{2 \times 1} \\ 0_{2 \times 2} & {\bar{W}}_{1,{({imod4})}} \\ 0_{2 \times 2} & 0_{2 \times 1} \end{bmatrix}\]

16 – 23

\[\frac{1}{2}\begin{bmatrix} {\bar{W}}_{2,{\lfloor{{(i - 16)}/4}\rfloor}} & 0_{2 \times 1} \\ 0_{2 \times 2} & 0_{2 \times 1} \\ 0_{2 \times 2} & 0_{2 \times 1} \\ 0_{2 \times 2} & {\bar{W}}_{1,{({imod4})}} \end{bmatrix}\]

24 – 31

\[\frac{1}{2}\begin{bmatrix} 0_{2 \times 2} & 0_{2 \times 1} \\ {\bar{W}}_{2,{\lfloor{{(i - 24)}/4}\rfloor}} & 0_{2 \times 1} \\ 0_{2 \times 2} & {\bar{W}}_{1,{({imod4})}} \\ 0_{2 \times 2} & 0_{2 \times 1} \end{bmatrix}\]

32 – 39

\[\frac{1}{2}\begin{bmatrix} 0_{2 \times 2} & 0_{2 \times 1} \\ {\bar{W}}_{2,{\lfloor{{(i - 32)}/4}\rfloor}} & 0_{2 \times 1} \\ 0_{2 \times 2} & 0_{2 \times 1} \\ 0_{2 \times 2} & {\bar{W}}_{1,{({imod4})}} \end{bmatrix}\]

40 – 47

\[\frac{1}{2}\begin{bmatrix} 0_{2 \times 2} & 0_{2 \times 1} \\ 0_{2 \times 2} & 0_{2 \times 1} \\ {\bar{W}}_{2,{\lfloor{{(i - 40)}/4}\rfloor}} & 0_{2 \times 1} \\ 0_{2 \times 2} & {\bar{W}}_{1,{({imod4})}} \end{bmatrix}\]

48 – 111

\[\frac{1}{2}\begin{bmatrix} {\bar{W}}_{1,{\lfloor{{(i - 48)}/16}\rfloor}} & 0_{2 \times 1} & 0_{2 \times 1} \\ 0_{2 \times 1} & {\bar{W}}_{1,{\lfloor{{(i\text{mod}16)}/4}\rfloor}} & 0_{2 \times 1} \\ 0_{2 \times 1} & 0_{2 \times 1} & {\bar{W}}_{1,{({imod4})}} \\ 0_{2 \times 1} & 0_{2 \times 1} & 0_{2 \times 1} \end{bmatrix}\]

112 – 175

\[\frac{1}{2}\begin{bmatrix} {\bar{W}}_{1,{\lfloor{{(i - 112)}/16}\rfloor}} & 0_{2 \times 1} & 0_{2 \times 1} \\ 0_{2 \times 1} & {\bar{W}}_{1,{\lfloor{{(i\text{mod}16)}/4}\rfloor}} & 0_{2 \times 1} \\ 0_{2 \times 1} & 0_{2 \times 1} & 0_{2 \times 1} \\ 0_{2 \times 1} & 0_{2 \times 1} & {\bar{W}}_{1,{({imod4})}} \end{bmatrix}\]

176 – 239

\[\frac{1}{2}\begin{bmatrix} {\bar{W}}_{1,{\lfloor{{(i - 176)}/16}\rfloor}} & 0_{2 \times 1} & 0_{2 \times 1} \\ 0_{2 \times 1} & 0_{2 \times 1} & 0_{2 \times 1} \\ 0_{2 \times 1} & {\bar{W}}_{1,{\lfloor{{(i\text{mod}16)}/4}\rfloor}} & 0_{2 \times 1} \\ 0_{2 \times 1} & 0_{2 \times 1} & {\bar{W}}_{1,{({imod4})}} \end{bmatrix}\]

240 – 303

\[\frac{1}{2}\begin{bmatrix} 0_{2 \times 1} & 0_{2 \times 1} & 0_{2 \times 1} \\ {\bar{W}}_{1,{\lfloor{{(i - 240)}/16}\rfloor}} & 0_{2 \times 1} & 0_{2 \times 1} \\ 0_{2 \times 1} & {\bar{W}}_{1,{\lfloor{{(i\text{mod}16)}/4}\rfloor}} & 0_{2 \times 1} \\ 0_{2 \times 1} & 0_{2 \times 1} & {\bar{W}}_{1,{({imod4})}} \end{bmatrix}\]

304

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 & 0 & 0 \\ 1 & 0 & 0 \\ 1 & 0 & 0 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 1 \end{bmatrix}\]

 

Table 6.3.1.5-42: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook3 and four-layer transmission using eight antenna ports with transform precoding disabled.

TPMI index \(\mathbf{i}\)

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)

0 – 255

\[\frac{1}{2}\begin{bmatrix} {\bar{W}}_{1,{\lfloor{i/64}\rfloor}} & 0_{2 \times 1} & 0_{2 \times 1} & 0_{2 \times 1} \\ 0_{2 \times 1} & {\bar{W}}_{1,{\lfloor{{(i\text{mod}64)}/16}\rfloor}} & 0_{2 \times 1} & 0_{2 \times 1} \\ 0_{2 \times 1} & 0_{2 \times 1} & {\bar{W}}_{1,{\lfloor{{(i\text{mod}16)}/4}\rfloor}} & 0_{2 \times 1} \\ 0_{2 \times 1} & 0_{2 \times 1} & 0_{2 \times 1} & {\bar{W}}_{1,{({imod4})}} \end{bmatrix}\]

256 – 259

\[\frac{1}{2}\begin{bmatrix} {\bar{W}}_{2,{\lfloor{{(i - 256)}/2}\rfloor}} & 0_{2 \times 2} \\ 0_{2 \times 2} & {\bar{W}}_{2,{({imod2})}} \\ 0_{2 \times 2} & 0_{2 \times 2} \\ 0_{2 \times 2} & 0_{2 \times 2} \end{bmatrix}\]

260 – 263

\[\frac{1}{2}\begin{bmatrix} {\bar{W}}_{2,{\lfloor{{(i - 260)}/2}\rfloor}} & 0_{2 \times 2} \\ 0_{2 \times 2} & 0_{2 \times 2} \\ 0_{2 \times 2} & {\bar{W}}_{2,{({imod2})}} \\ 0_{2 \times 2} & 0_{2 \times 2} \end{bmatrix}\]

264 – 267

\[\frac{1}{2}\begin{bmatrix} {\bar{W}}_{2,{\lfloor{{(i - 264)}/2}\rfloor}} & 0_{2 \times 2} \\ 0_{2 \times 2} & 0_{2 \times 2} \\ 0_{2 \times 2} & 0_{2 \times 2} \\ 0_{2 \times 2} & {\bar{W}}_{2,{({imod2})}} \end{bmatrix}\]

268 – 271

\[\frac{1}{2}\begin{bmatrix} 0_{2 \times 2} & 0_{2 \times 2} \\ {\bar{W}}_{2,{\lfloor{{(i - 268)}/2}\rfloor}} & 0_{2 \times 2} \\ 0_{2 \times 2} & {\bar{W}}_{2,{({imod2})}} \\ 0_{2 \times 2} & 0_{2 \times 2} \end{bmatrix}\]

272 – 275

\[\frac{1}{2}\begin{bmatrix} 0_{2 \times 2} & 0_{2 \times 2} \\ {\bar{W}}_{2,{\lfloor{{(i - 272)}/2}\rfloor}} & 0_{2 \times 2} \\ 0_{2 \times 2} & 0_{2 \times 2} \\ 0_{2 \times 2} & {\bar{W}}_{2,{({imod2})}} \end{bmatrix}\]

276 – 279

\[\frac{1}{2}\begin{bmatrix} 0_{2 \times 2} & 0_{2 \times 2} \\ 0_{2 \times 2} & 0_{2 \times 2} \\ {\bar{W}}_{2,{\lfloor{{(i - 276)}/2}\rfloor}} & 0_{2 \times 2} \\ 0_{2 \times 2} & {\bar{W}}_{2,{({imod2})}} \end{bmatrix}\]

 

Table 6.3.1.5-43: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook3 and five-layer transmission using eight antenna ports with transform precoding disabled.

TPMI index \(\mathbf{i}\)

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)

0 – 15

\[\frac{1}{2}\begin{bmatrix} {\bar{W}}_{2,{\lfloor{i/8}\rfloor}} & 0_{2 \times 2} & 0_{2 \times 1} \\ 0_{2 \times 2} & 0_{2 \times 2} & 0_{2 \times 1} \\ 0_{2 \times 2} & {\bar{W}}_{2,{\lfloor{{({imod8})}/4}\rfloor}} & 0_{2 \times 1} \\ 0_{2 \times 2} & 0_{2 \times 2} & {\bar{W}}_{1,{({imod4})}} \end{bmatrix}\]

16 – 31

\[\frac{1}{2}\begin{bmatrix} 0_{2 \times 2} & 0_{2 \times 2} & 0_{2 \times 1} \\ {\bar{W}}_{2,{\lfloor{{(i - 16)}/8}\rfloor}} & 0_{2 \times 2} & 0_{2 \times 1} \\ 0_{2 \times 2} & {\bar{W}}_{2,{\lfloor{{({imod8})}/4}\rfloor}} & 0_{2 \times 1} \\ 0_{2 \times 2} & 0_{2 \times 2} & {\bar{W}}_{1,{({imod4})}} \end{bmatrix}\]

32 – 159

\[\frac{1}{2}\begin{bmatrix} {\bar{W}}_{1,{\lfloor{{(i - 32)}/32}\rfloor}} & 0_{2 \times 1} & 0_{2 \times 2} & 0_{2 \times 1} \\ 0_{2 \times 1} & {\bar{W}}_{1,{\lfloor{{({imod32})}/8}\rfloor}} & 0_{2 \times 2} & 0_{2 \times 1} \\ 0_{2 \times 1} & 0_{2 \times 1} & {\bar{W}}_{2,{\lfloor{{({imod8})}/4}\rfloor}} & 0_{2 \times 1} \\ 0_{2 \times 1} & 0_{2 \times 1} & 0_{2 \times 2} & {\bar{W}}_{1,{({imod4})}} \end{bmatrix}\]

 

Table 6.3.1.5-44: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook3 and six-layer transmission using eight antenna ports with transform precoding disabled.

TPMI index \(\mathbf{i}\)

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)

0 – 7

\[\frac{1}{2}\begin{bmatrix} {\bar{W}}_{2,{\lfloor{i/4}\rfloor}} & 0_{2 \times 2} & 0_{2 \times 2} \\ 0_{2 \times 2} & {\bar{W}}_{2,{\lfloor{{({imod4})}/2}\rfloor}} & 0_{2 \times 2} \\ 0_{2 \times 2} & 0_{2 \times 2} & {\bar{W}}_{2,{({imod2})}} \\ 0_{2 \times 2} & 0_{2 \times 2} & 0_{2 \times 2} \end{bmatrix}\]

8 – 15

\[\frac{1}{2}\begin{bmatrix} {\bar{W}}_{2,{\lfloor{{(i - 8)}/4}\rfloor}} & 0_{2 \times 2} & 0_{2 \times 2} \\ 0_{2 \times 2} & 0_{2 \times 2} & 0_{2 \times 2} \\ 0_{2 \times 2} & {\bar{W}}_{2,{\lfloor{{({imod4})}/2}\rfloor}} & 0_{2 \times 2} \\ 0_{2 \times 2} & 0_{2 \times 2} & {\bar{W}}_{2,{({imod2})}} \end{bmatrix}\]

16 – 79

\[\frac{1}{2}\begin{bmatrix} {\bar{W}}_{2,{\lfloor{{(i - 16)}/32}\rfloor}} & 0_{2 \times 1} & 0_{2 \times 2} & 0_{2 \times 1} \\ 0_{2 \times 2} & {\bar{W}}_{1,{\lfloor{{({{({i - 16})}mod32})}/8}\rfloor}} & 0_{2 \times 2} & 0_{2 \times 1} \\ 0_{2 \times 2} & 0_{2 \times 1} & {\bar{W}}_{2,{\lfloor{{({imod8})}/4}\rfloor}} & 0_{2 \times 1} \\ 0_{2 \times 2} & 0_{2 \times 1} & 0_{2 \times 2} & {\bar{W}}_{1,{({imod4})}} \end{bmatrix}\]

 

Table 6.3.1.5-45: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook3 and seven-layer transmission using eight antenna ports with transform precoding disabled.

TPMI index \(\mathbf{i}\)

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)

0 – 31

\[\frac{1}{2}\begin{bmatrix} {\bar{W}}_{2,{\lfloor{i/16}\rfloor}} & 0_{2 \times 1} & 0_{2 \times 2} & 0_{2 \times 2} \\ 0_{2 \times 2} & {\bar{W}}_{1,{\lfloor{{({imod16})}/4}\rfloor}} & 0_{2 \times 2} & 0_{2 \times 2} \\ 0_{2 \times 2} & 0_{2 \times 1} & {\bar{W}}_{2,{\lfloor{{({imod4})}/2}\rfloor}} & 0_{2 \times 2} \\ 0_{2 \times 2} & 0_{2 \times 1} & 0_{2 \times 2} & {\bar{W}}_{2,{({imod2})}} \end{bmatrix}\]

 

Table 6.3.1.5-46: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook3 and eight-layer transmission using eight antenna ports with transform precoding disabled.

TPMI index \(\mathbf{i}\)

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)

0 – 15

\[\frac{1}{2}\begin{bmatrix} {\bar{W}}_{2,{\lfloor{i/8}\rfloor}} & 0_{2 \times 2} & 0_{2 \times 2} & 0_{2 \times 2} \\ 0_{2 \times 2} & {\bar{W}}_{2,{\lfloor{{({imod8})}/4}\rfloor}} & 0_{2 \times 2} & 0_{2 \times 2} \\ 0_{2 \times 2} & 0_{2 \times 2} & {\bar{W}}_{2,{\lfloor{{({imod4})}/2}\rfloor}} & 0_{2 \times 2} \\ 0_{2 \times 2} & 0_{2 \times 2} & 0_{2 \times 2} & {\bar{W}}_{2,{({imod2})}} \end{bmatrix}\]

 

Table 6.3.1.5-47: Intermediate precoding matrix \(\mathbf{W}\mathbf{'}\) for codebook4 and transmission using eight antenna ports. Up to 8 layers are supported with transform precoding disabled="disabled" and up to one layer with transform precoding enabled.

TPMI index

Intermediate precoder matrix \(\mathbf{W}\mathbf{'}\)

0 – \(\Delta(\nu) - 1\)

\[W' = \frac{1}{2\sqrt[{}]{2}}\left\lbrack e_{p_{0}}\ldots e_{p_{\nu - 1}} \right\rbrack\]

 

where column \(i\) of \(W'\), denoted \(e_{i}\), has an element 1 on the row corresponding to the port \(p_{i}\) on which layer \(i\) is to be transmitted, and element 0 in all other rows, \(p_{i} < p_{i + 1}\),

\(L = \sum\limits_{p = 0}^{7}{\delta(p)2}^{p}\), where \(\delta(p) = 1\) if a layer is to be transmitted on port \(p\) and \(\delta(p) = 0\) otherwise, and \(\Delta(z) = \sum\limits_{k = 1}^{z}{C(8,k)}\) for \(z \geq 1\), where \(C\left( {x,y} \right)\) is defined by Table 5.2.2.2.5-4 of [6, TS 38.214].

 

TPMI indices \(0\) to \(\Delta(\nu) - 1\) are mapped to values of \(L\), first by increasing values of the number of transmitted layers, and then by increasing values of \(L\) for a given number of layers.

255

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} 1 \\ 1 \end{matrix} \\ 1 \\ 1 \end{matrix} \\ 1 \end{matrix} \\ 1 \\ 1 \end{matrix} \\ 1 \end{bmatrix}\]

256

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} 1 \\ 1 \end{matrix} \\ 0 \\ 0 \end{matrix} \\ 1 \end{matrix} \\ 1 \\ 0 \end{matrix} \\ 0 \end{matrix} & \begin{matrix} 0 \\ 0 \\ \begin{matrix} 1 \\ 1 \\ \begin{matrix} 0 \\ 0 \\ \begin{matrix} 1 \\ 1 \end{matrix} \end{matrix} \end{matrix} \end{matrix} \end{bmatrix}\]

257

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 & 0 & 0 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}\]

258

\[\frac{1}{2\sqrt[{}]{2}}\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}\]

 

Table 6.3.1.5-48: Precoding matrix \(\mathbf{W}\) for single-layer transmission using three antenna ports with 4portSRS_3TX configured.

TPMI index

Precoder matrix \(\mathbf{W}\)(ordered from left to right in increasing order of TPMI index)

0 – 2

\[\frac{1}{\sqrt[{}]{3}}\begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}\]

\[\frac{1}{\sqrt[{}]{3}}\begin{bmatrix} 0 \\ 1 \\ 0 \end{bmatrix}\]

\[\frac{1}{\sqrt[{}]{3}}\begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix}\]

-

-

-

-

-

 

Table 6.3.1.5-49: Precoding matrix \(\mathbf{W}\) for two-layer transmission using three antenna ports with 4portSRS_3TX configured.

TPMI index

Precoder matrix \(\mathbf{W}\)(ordered from left to right in increasing order of TPMI index)<br>

0 – 2

\[\frac{1}{\sqrt[{}]{3}}\begin{bmatrix} 1 & 0 \\ 0 & 1 \\ 0 & 0 \end{bmatrix}\]

\[\frac{1}{\sqrt[{}]{3}}\begin{bmatrix} 1 & 0 \\ 0 & 0 \\ 0 & 1 \end{bmatrix}\]

\[\frac{1}{\sqrt[{}]{3}}\begin{bmatrix} 0 & 0 \\ 1 & 0 \\ 0 & 1 \end{bmatrix}\]

-

 

Table 6.3.1.5-50: Precoding matrix \(\mathbf{W}\) for three-layer transmission using three antenna ports with 4portSRS_3TX configured.

TPMI index

Precoder matrix \(\mathbf{W}\)(ordered from left to right in increasing order of TPMI index)<br>

0

\[\frac{1}{\sqrt[{}]{3}}\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}\]

-

-

-

 

6 .3.1.6    Mapping to virtual resource blocks #

For each of the antenna ports used for transmission of the PUSCH, each symbol in the block of complex-valued symbols \(z^{(p)}(0),\ldots,z^{(p)}\bigl(M_{\mathrm{symb}}^{\mathrm{ap}}-1\bigr)\) shall be multiplied with \(\sqrt[{}]{2}\) if the symbol corresponds to an OFDM symbol occupied by a muting resource, and by 1 otherwise, and further be multiplied with the amplitude scaling factor \(\beta_{\mathrm{PUSCH}}\) in order to conform to the transmit power specified in [5, TS 38.213] and mapped in sequence starting with \(z^{(p)}(0)\) to resource elements \((k',l)_{p,\mu}\) in the virtual resource blocks assigned for transmission which meet all of the following criteria:

-    they are in the virtual resource blocks assigned for transmission, and

-    the corresponding resource elements in the corresponding physical resource blocks are not used for transmission of the associated DM-RS, PT-RS, or DM-RS intended for other co-scheduled UEs as described in clause 6.4.1.1.3, and

-    the corresponding resource elements in the corresponding physical resource blocks do not correspond to a muting resource.

The mapping to resource elements \((k',l)_{p,\mu}\) allocated for PUSCH according to [6, TS 38.214] shall be in increasing order of first the index \(k'\) over the assigned virtual resource blocks, where \(k^{'} = 0\) is the first subcarrier in the lowest-numbered virtual resource block assigned for transmission, and then the index \(l\), with the starting position given by [6, TS 38.214].

6.3.1. 7    Mapping from virtual to physical resource blocks #

Virtual resource blocks shall be mapped to physical resource blocks according to non-interleaved mapping.

For non-interleaved VRB-to-PRB mapping for uplink resource allocation types 0 and 1 [6, TS 38.214], virtual resource block \(n\) is mapped to physical resource block \(n\) except for PUSCH scheduled by RAR UL grant or PUSCH scheduled by DCI format 0_0 with CRC scrambled by TC-RNTI in active uplink bandwidth part \(i\) starting at \(N_{\text{BWP},i}^{\text{start}}\), including all resource blocks of the initial uplink bandwidth part starting at \(N_{\text{BWP},0}^{\text{start}}\), and having the same subcarrier spacing and cyclic prefix as the initial uplink bandwidth part, in which case virtual resource block \(n\) is mapped to physical resource block \(n + N_{\text{BWP},0}^{\text{start}} - N_{\text{BWP},i}^{\text{start}}\).

For non-interleaved VRB-to-PRB mapping for uplink resource allocation type 2 [6, TS 38.214], virtual resource block \(n\) is mapped to physical resource block \(n\).

6.3.2.1     General #

The physical uplink control channel supports multiple="multiple" formats as shown in Table 6.3.2.1-1. In case intra-slot frequency hopping is configured for PUCCH formats 1, 3, or 4 according to clause 9.2.1 of [5, TS38.213], the number of symbols in the first hop is given by \(\left\lceil \frac{N^{\mathrm{PUCCH}}_{\mathrm{symb}}}{2} \right\rceil\) where \(N_{\mathrm{symb}}^{\mathrm{PUCCH}}\) is the length of the PUCCH transmission in OFDM symbols.

Table 6.3.2.1-1: PUCCH formats.

PUCCH format

Length in OFDM symbols \(N_{\mathrm{symb}}^{\mathrm{PUCCH}}\)

Number of bits

0

1 – 2

≤2

1

4 – 14

≤2

2

1 – 2

>2

3

4 – 14

>2

4

4 – 14

>2

 

6.3.2.2     Sequence and cyclic shift hopping #

PUCCH formats 0, 1, 3, and 4 use sequences \(r_{u,v}^{({\alpha,\delta})}(n)\) given by clause 5.2.2 with \(\delta = 0\) where the sequence group \(u\) and the sequence number \(v\) depend on the sequence hopping in clause 6.3.2.2.1 and the cyclic shift \(\alpha\) depends on the cyclic shift hopping in clause 6.3.2.2.2.

6.3.2.2.1     Group and sequence hopping #

The sequence group \(u = \left( {f_{\text{gh}} + f_{\text{ss}}} \right)\text{mod}30\) and the sequence number \(v\) within the group depends on the higher-layer parameter pucch-GroupHopping:

-    if pucch-GroupHopping equals 'neither'

\(\begin{aligned} f_{gh} &= 0\\ f_{ss} &= n_{\mathrm{ID}} \bmod 30\\ v &= 0 \end{aligned}\)

    where \(n_{ID}\) is given by the higher-layer parameter hoppingId if configured, otherwise \(n_{\text{ID}} = N_{\text{ID}}^{\text{cell}}\).

-    if pucch-GroupHopping equals 'enable'

\(f_{gh}=\left(\sum_{m=0}^{7}2^{m}c\!\left(8\bigl(2n_{s,f}^{\mu}+n_{hop}\bigr)+m\right)\right)\bmod 30 f_{ss}=n_{ID}\bmod 30 v=0\)

    where the pseudo-random sequence \(c(i)\) is defined by clause 5.2.1 and shall be initialized at the beginning of each radio frame with \(c_{\text{init}}=\left[\frac{n_{\text{ID}}}{30}\right]\) where \(n_{ID}\) is given by the higher-layer parameter hoppingId if configured, otherwise \(n_{\text{ID}} = N_{\text{ID}}^{\text{cell}}\).

-    if pucch-GroupHopping equals 'disable'

\(\[ \begin{aligned} f_{gh} &= 0 \\ f_{ss} &= n_{\mathrm{ID}} \bmod 30 \\ \nu &= c\left(2n_{s,f}^{\mu} + n_{hop}\right) \end{aligned} \]\)

    where the pseudo-random sequence \(c(i)\) is defined by clause 5.2.1 and shall be initialized at the beginning of each radio frame with \(c_{\text{init}} = 2^{5}\left\lfloor {n_{\text{ID}}/30} \right\rfloor + \left( {n_{\text{ID}}\text{mod}30} \right)\) where \(n_{ID}\) is given by the higher-layer parameter hoppingId if configured, otherwise \(n_{\text{ID}} = N_{\text{ID}}^{\text{cell}}\).

The frequency hopping index \(n_{\text{hop}} = 0\) if intra-slot frequency hopping is disabled="disabled" by the higher-layer parameter intraSlotFrequencyHopping. If frequency hopping is enabled by the higher-layer parameter intraSlotFrequencyHopping, \(n_{\mathrm{hop}}=0\) for the first hop and \(n_{\mathrm{hop}} = 1\) for the second hop.

6.3.2.2.2     Cyclic shift hopping #

The cyclic shift \(\alpha\) varies as a function of the symbol and slot number according to

\[\alpha_{l} = \frac{2\pi}{N_{\text{sc}}^{\text{RB}}}\left( {\left( {m_{0} + m_{\text{cs}} + m_{\text{int}} + n_{\text{cs}}\left( {n_{\text{s,f}}^{\mu},l + l'} \right)} \right)\text{mod}N_{\text{sc}}^{\text{RB}}} \right)\]

where

-    \(n_{\text{s,f}}^{\mu}\) is the slot number in the radio frame

-    \(l\) is the OFDM symbol number in the PUCCH transmission where \(l = 0\) corresponds to the first OFDM symbol of the PUCCH transmission,

-    \(l'\) is the index of the OFDM symbol in the slot that corresponds to the first OFDM symbol of the PUCCH transmission in the slot given by [5, TS 38.213]

-    \(m_{0}\) is given by [5, TS 38.213] for PUCCH format 0 and 1 while for PUCCH format 3 and 4 is defined in clause 6.4.1.3.3.1

-    \(m_{cs}=0\) except for PUCCH format 0 when it depends on the information to be transmitted according to clause 9.2 of [5, TS 38.213].

-    \(m_{\text{int}}\) is given by

-    \(m_{\text{int}} = {5n}_{\text{IRB}}^{\mu}\) for PUCCH formats 0 and 1 if PUCCH shall use interlaced mapping according to any of the higher-layer parameters useInterlacePUCCH-PUSCH in BWP-UplinkCommon or useInterlacePUCCH-PUSCH in BWP-UplinkDedicated, where \(n_{\text{IRB}}^{\mu}\) is the resource block number within the interlace;

-    \(m_{\text{int}} = 0\) otherwise

The function \(n_{cs}(n_c,l)\) is given by

    \(n_{\text{cs}}\left( {n_{\text{s,f}}^{\mu},l} \right) = \sum\limits_{m = 0}^{7}2^{m}c\left( {8N_{\text{symb}}^{\text{slot}}n_{\text{s,f}}^{\mu} + 8l + m} \right)\)

where the pseudo-random sequence \(c(i)\) is defined by clause 5.2.1. The pseudo-random sequence generator shall be initialized with \(c_{\text{init}} = n_{\text{ID}}\), where \(n_{ID}\) is given by the higher-layer parameter hoppingId if configured, otherwise \(n_{\text{ID}} = N_{\text{ID}}^{\text{cell}}\).

6.3.2. 3    PUCCH format 0 #

6.3.2. 3.1    Sequence generation #

The sequence \(x(n)\) shall be generated according to

xlMRBPUCCH,0NscRB+n=ru,vα,δnn=0,1,,MRBPUCCH,0NscRB-1l=0for single-symbol PUCCH transmission0,1for double-symbol PUCCH transmission

where \(r_{u,v}^{({\alpha,\delta})}(n)\) is given by clause 6.3.2.2 with \(m_{cs}\) depending on the information to be transmitted according to clause 9.2 of [5, TS 38.213]. The quantity \(M_{\text{RB}}^{\text{PUCCH,}0}\) is given by clause 9.2.1 of [5, TS 38.213].

6.3.2. 3.2    Mapping to physical resources #

The sequence \(x(n)\) shall be multiplied with the amplitude scaling factor \(\beta_{\mathrm{PUCCH},0}\) in order to conform to the transmit power specified in [5, TS 38.213] and mapped in sequence starting with \(x(0)\) to resource elements \(\left( {k,l} \right)_{p,\mu}\) assigned for transmission according to clause 9.2.1 of [5, TS 38.213] in increasing order of first the index \(k\) over the assigned physical resources spanning \(M_{\text{RB}}^{\text{PUCCH,}0}\) resource blocks, and then the index \(l\) on antenna port \(p = 2000\).

For interlaced transmission, the mapping operation shall be repeated for each resource block in the interlace and in the active bandwidth part over the assigned physical resource blocks according to clause 9.2.1 of [5, TS 38.213], with the resource-block dependent sequence generated according to clause 6.3.2.2.

6.3.2. 4    PUCCH format 1 #

6.3.2. 4.1    Sequence modulation #

The block of bits \(b(0),\ldots,b(M_{bit}-1)\) shall be modulated as described in clause 5.1 using BPSK if \(M_{bit}=1\) and QPSK if \(M_{bit}=2\), resulting in a complex-valued symbol \(d(0)\). The complex-valued symbol <br>\(d(0)\) shall be multiplied with a sequence \(r_{u,v}^{({\alpha,\delta})}(n)\) according to

\[\begin{matrix} {y(n) = d(0)r_{u,v}^{({\alpha,\delta})}(n)} \\ {n = 0,1,\ldots,M_{\text{RB}}^{\text{PUCCH},1}N_{\text{sc}}^{\text{RB}} - 1} \end{matrix}\]

where \(r_{u,v}^{({\alpha,\delta})}(n)\) is given by clause 6.3.2.2. The quantity \(M_{\text{RB}}^{\text{PUCCH,}1}\) is given by clause 9.2.1 of [5, TS 38.213].

The block of complex-valued symbols \(y(0),\ldots,y\left( {M_{\text{RB}}^{\text{PUCCH},1}N_{\text{sc}}^{\text{RB}} - 1} \right)\) shall be block-wise spread with the orthogonal sequence \(w_i(m)\) according to

zm'MRBPUCCH,1NscRBNSF,0PUCCH,1+mMRBPUCCH,1NscRB+n=wimynn=0,1,,MRBPUCCH,1NscRB-1m=0,1,,NSF,m'PUCCH,1-1m'=0no intra-slot frequency hopping0,1intra-slot frequency hopping

where \(N_{\text{SF},m'}^{\text{PUCCH},1}\) is given by Table 6.3.2.4.1-1. Intra-slot frequency hopping shall be assumed when the higher-layer parameter intraSlotFrequencyHopping is provided, regardless of whether the frequency-hop distance is zero or not, and interlaced mapping is not enabled, otherwise no intra-slot frequency hopping shall be assumed.

The orthogonal sequence \(w_i(m)\) is given by Table 6.3.2.4.1-2 where \(i\) is the index of the orthogonal sequence to use according to clause 9.2.1 of [5, TS 38.213]. In case of a PUCCH transmission spanning multiple="multiple" slots according to clause 9.2.6 of [5, TS38.213], the complex-valued symbol \(d(0)\) is repeated for the subsequent slots.

Table 6.3.2.4.1-1: Number of PUCCH symbols and the corresponding \(N^{\mathrm{PUCCH},1}_{\mathrm{SF},\,m'}\).

PUCCH length, <br>\(N_{\mathrm{symb}}^{\mathrm{PUCCH,1}}\)

\(N^{\mathrm{PUCCH},1}_{\mathrm{SF},\,m'}\)

No intra-slot hopping

\(m' = 0\)

Intra-slot hopping

\(m' = 0\)

\(m'=1\)

4

2

1

1

5

2

1

1

6

3

1

2

7

3

1

2

8

4

2

2

9

4

2

2

10

5

2

3

11

5

2

3

12

6

3

3

13

6

3

3

14

7

3

4

 

Table 6.3.2.4.1-2: Orthogonal sequences \(w_i(m)=e^{j\,2\pi\phi(m)\,/\,N_{\mathrm{SF},m'}^{\mathrm{PUCCH},1}}\) for PUCCH format 1.

\(N^{\mathrm{PUCCH},1}_{\mathrm{SF},\,m'}\)

\(\phi\)

\(i=0\)

\(i=1\)

\(i=2\)

\(i=3\)

\(\[i=4\]\)

\(i=5\)

\(i=6\)

1

[0]

-

-

-

-

-

-

2

[0 0]

[0 1]

-

-

-

-

-

3

[0 0 0]

[0 1 2]

[0 2 1]

-

-

-

-

4

[0 0 0 0]

[0 2 0 2]

[0 0 2 2]

[0 2 2 0]

-

-

-

5

[0 0 0 0 0]

[0 1 2 3 4]

[0 2 4 1 3]

[0 3 1 4 2]

[0 4 3 2 1]

-

-

6

[0 0 0 0 0 0]

[0 1 2 3 4 5]

[0 2 4 0 2 4]

[0 3 0 3 0 3]

[0 4 2 0 4 2]

[0 5 4 3 2 1]

-

7

[0 0 0 0 0 0 0]

[0 1 2 3 4 5 6]

[0 2 4 6 1 3 5]

[0 3 6 2 5 1 4]

[0 4 1 5 2 6 3]

[0 5 3 1 6 4 2]

[0 6 5 4 3 2 1]

 

6.3.2. 4.2    Mapping to physical resources #

The sequence \(z(n)\) shall be multiplied with the amplitude scaling factor \(\beta_{\text{PUCCH,1}}\) in order to conform to the transmit power specified in [5, TS 38.213] and mapped in sequence starting with \(z(n)\) to resource elements \(\left( {k,l} \right)_{p,\mu}\) which meet all of the following criteria:

-    they are in the resource blocks assigned for transmission,

-    they are not used by the associated DM-RS

The mapping to resource elements \(\left( {k,l} \right)_{p,\mu}\) not reserved for other purposes shall be in increasing order of first the index \(k\) over the assigned physical resource blocks according to clause 9.2.1 of [5, TS 38.213], and then the index \(l\) on antenna port \(p = 2000\).

For interlaced transmission, the mapping operation shall be repeated for each resource block in the interlace and in the active bandwidth part over the assigned physical resource blocks according to clause 9.2.1 of [5, TS 38.213], with the resource-block dependent sequence generated according to clause 6.3.2.2.

6.3.2. 5    PUCCH format 2 #

6.3.2. 5.1    Scrambling #

The block of bits \(b(0),\ldots,b\left( M_{\text{bit}} - 1 \right)\), where \(M_{\text{bit}}\) is the number of bits transmitted on the physical channel, shall be scrambled prior to modulation, resulting in a block of scrambled bits \(\overset{\sim}{b}(0),\ldots,\overset{\sim}{b}\left( M_{\text{bit}} - 1 \right)\) according to the following pseudo code

Set i = 0

while \(i < M_{\text{bit}}\)

if \(b(i) = y\)    // UCI placeholder bits

\(\overset{\sim}{b}(i) = \overset{\sim}{b}\left( {i - 1} \right)\)

else

\(\overset{\sim}{b}(i) = \left( {b(i) + c(i)} \right)\text{mod}2\)

end if

i = i + 1

end while

where y is the tag defined in [4, TS38.212] and the scrambling sequence \(c(i)\) is given by clause 5.2.1. The scrambling sequence generator shall be initialized with

\[c_{\text{init}} = n_{\text{RNTI}} \bullet 2^{15} + n_{\text{ID}}\]

where

-    \(n_{\text{ID}} \in \left\{ {0,1,\ldots,1023} \right\}\) equals the higher-layer parameter dataScramblingIdentityPUSCH if configured,

-    \(n_{\text{ID}} = N_{\text{ID}}^{\text{cell}}\) otherwise

and \(n_{\text{RNTI}}\) is given by the C-RNTI.

6.3.2. 5.2    Modulation #

The block of scrambled bits \(\overset{\sim}{b}(0),\ldots,\overset{\sim}{b}\left( M_{\text{bit}} - 1 \right)\) shall be modulated as described in clause 5.1 using QPSK, resulting in a block of complex-valued modulation symbols \(d(0),\ldots,d\left( M_{\text{symb}} - 1 \right)\) where \(M_{\text{symb}} = {M_{\text{bit}}/2}\).

6.3.2.5.2A     Spreading #

Spreading shall be applied according to

\[\begin{matrix} {z\left( {mN_{\text{SF}}^{\text{PUCCH,2}} + i} \right) = w_{n}(i)d(m)} \\ {i = 0,1,\ldots,N_{\text{SF}}^{\text{PUCCH,2}} - 1} \\ {m = 0,1,\ldots,M_{\text{symb}} - 1} \end{matrix}\]

resulting in a block of complex-valued symbols \(z(0),\ldots,z\left( N_{\text{SF}}^{\text{PUCCH,}2}M_{\text{symb}} - 1 \right)\).

If the higher layer parameter interlace1 is not configured, and the higher-layer parameter occ-Length is configured,

-    \(N_{\text{SF}}^{\text{PUCCH,}2} \in \left\{ 2,4 \right\}\) is given by the higher-layer parameter occ-Length;

-    \(w_{n}(i)\) is given by Tables 6.3.2.5A-1 and 6.3.2.5A-2 where \(n = \left( {n_{0} + n_{\text{IRB}}} \right)\text{mod}N_{\text{SF}}^{\text{PUCCH,}2}\), the quantity \(n_{0}\) is the index of the orthogonal sequence to use given by the higher-layer parameter occ-Index, and \(n_{\text{IRB}}\) is the interlaced resource block number as defined in clause 4.4.4.6 within the interlace given by the higher-layer parameter Interlace0.

otherwise \(N_{\text{SF}}^{\text{PUCCH,}2} = 1\) and \(w_{n}(i) = 1.\)

Table 6.3.2.5A-1: Orthogonal sequences \(\mathbf{w}_{\mathbf{n}}\left( \mathbf{i} \right)\) for PUCCH format 2 when \(\mathbf{N}_{\text{SF}}^{\text{PUCCH,}2} = 2\).

\[\mathbf{n}\]

\[\mathbf{w}_{\mathbf{n}}\left( \mathbf{i} \right)\]

0

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

1

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

 

Table 6.3.2.5A-2: Orthogonal sequences \(\mathbf{w}_{\mathbf{n}}\left( \mathbf{i} \right)\) for PUCCH format 2 when \(\mathbf{N}_{\text{SF}}^{\text{PUCCH,}2} = 4\).

\[\mathbf{n}\]

\[\mathbf{w}_{\mathbf{n}}\left( \mathbf{i} \right)\]

0

\[\begin{bmatrix} {+ 1} & {+ 1} & {+ 1} & {+ 1} \end{bmatrix}\]

1

\[\begin{bmatrix} {+ 1} & {- 1} & {+ 1} & {- 1} \end{bmatrix}\]

2

\[\begin{bmatrix} {+ 1} & {+ 1} & {- 1} & {- 1} \end{bmatrix}\]

3

\[\begin{bmatrix} {+ 1} & {- 1} & {- 1} & {+ 1} \end{bmatrix}\]

 

6.3.2. 5.3    Mapping to physical resources #

The block of complex-valued symbols \(z(0),\ldots,z\left( N_{\text{SF}}^{\text{PUCCH,}2}M_{\text{symb}} - 1 \right)\) shall be multiplied with the amplitude scaling factor \(\beta_{\mathrm{PUCCH},2}\) in order to conform to the transmit power specified in [5, TS 38.213] and mapped in sequence starting with \(z(0)\) to resource elements \(\left( {k,l} \right)_{p,\mu}\) which meet all of the following criteria:

-    they are in the resource blocks assigned for transmission,

-    they are not used by the associated DM-RS.

The mapping to resource elements \(\left( {k,l} \right)_{p,\mu}\) not reserved for other purposes shall be in increasing order of first the index \(k\) over the assigned physical resource blocks according to clause 9.2.1 of [5, TS 38.213], and then the index \(l\) on antenna port \(p=2000\).

6.3.2. 6    PUCCH formats 3 and 4 #

6.3.2. 6.1    Scrambling #

The block of bits \(b(0),\ldots,b\left( M_{\text{bit}} - 1 \right)\), where \(M_{\text{bit}}\) is the number of bits transmitted on the physical channel, shall be scrambled prior to modulation, resulting in a block of scrambled bits \(\overset{\sim}{b}(0),\ldots,\overset{\sim}{b}\left( M_{\text{bit}} - 1 \right)\) according to the following pseudo code

Set i = 0

while \(i < M_{\text{bit}}\)

if \(b(i) = y\)    // UCI placeholder bits

\(\overset{\sim}{b}(i) = \overset{\sim}{b}\left( {i - 1} \right)\)

else

\(\overset{\sim}{b}(i) = \left( {b(i) + c(i)} \right)\text{mod}2\)

end if

i = i + 1

end while

where y is the tag defined in [4, TS38.212] and the scrambling sequence \(c(i)\) is given by clause 5.2.1. The scrambling sequence generator shall be initialized with

\[c_{\text{init}} = n_{\text{RNTI}} \bullet 2^{15} + n_{\text{ID}}\]

where

-    \(n_{\text{ID}} \in \left\{ {0,1,\ldots,1023} \right\}\) equals the higher-layer parameter dataScramblingIdentityPUSCH if configured,

-    \(n_{\text{ID}} = N_{\text{ID}}^{\text{cell}}\) otherwise

and \(n_{\text{RNTI}}\) is given by the C-RNTI.

6.3.2. 6.2    Modulation #

The block of scrambled bits \(\overset{\sim}{b}(0),\ldots,\overset{\sim}{b}\left( M_{\text{bit}} - 1 \right)\) shall be modulated as described in clause 5.1 using QPSK unless π/2-BPSK is configured, resulting in a block of complex-valued modulation symbols \(d(0),\ldots,d\left( M_{\text{symb}} - 1 \right)\) where \(M_{\text{symb}} = {M_{\text{bit}}/2}\) for QPSK and \(M_{\text{symb}} = M_{\text{bit}}\) for π/2-BPSK.

6.3.2. 6.3    Block-wise spreading #

For both PUCCH format 3 and 4, \(M_{\text{sc}}^{\text{PUCCH,}s} = M_{\text{RB}}^{\text{PUCCH,}s}N_{\text{sc}}^{\text{RB}}\) with \(M_{\text{RB}}^{\text{PUCCH,}s}\) representing the bandwidth of the PUCCH in terms of resource blocks according to clauses 9.2.3, 9.2.5.1 and 9.2.5.2 of [5, TS 38.213] and shall for non-interlaced mapping fulfil

    \(M_{\text{RB}}^{\text{PUCCH},s} = 2^{\alpha_{2}} \bullet 3^{\alpha_{3}} \bullet 5^{\alpha_{5}}\)

where \(a_2, a_3, a_5\) is a set of non-negative integers and \(s \in \{3,4\}\). For interlaced mapping, \(M_{\text{RB}}^{\text{PUCCH,}3} = 10\) if a single interlace is configured and \(M_{\text{RB}}^{\text{PUCCH,}3} = 20\) if two interlaces are configured.

For PUCCH format 3, if interlaced mapping is not configured, no block-wise spreading is applied and

\(\begin{aligned} y\bigl(l M_{sc}^{\mathrm{PUCCH},3} + k\bigr) &= d\bigl(l M_{sc}^{\mathrm{PUCCH},3} + k\bigr) \\ k &= 0,1,\ldots, M_{sc}^{\mathrm{PUCCH},3} - 1 \\ l &= 0,1,\ldots, \left( \frac{M_{\mathrm{symb}}}{M_{sc}^{\mathrm{PUCCH},3}} \right) - 1 \end{aligned}\)

where \(M_{\text{RB}}^{\text{PUCCH,}3} \geq 1\) is given by clauses 9.2.3, 9.2.5.1 and 9.2.5.2 of [5, TS 38.213] and \(N_{\text{SF}}^{\text{PUCCH,}3} = 1\).

For PUCCH format 3 with interlaced mapping and PUCCH format 4, block-wise spreading shall be applied according to

\[\begin{matrix} {y\left( {lM_{\text{sc}}^{\text{PUCCH},s} + k} \right) = w_{n}\left( \left\lfloor {k\frac{N_{\text{SF}}^{\text{PUCCH},s}}{M_{\text{sc}}^{\text{PUCCH},s}}} \right\rfloor \right)d\left( {l\frac{M_{\text{sc}}^{\text{PUCCH},s}}{N_{\text{SF}}^{\text{PUCCH},s}} + k\text{mod}\frac{M_{\text{sc}}^{\text{PUCCH},s}}{N_{\text{SF}}^{\text{PUCCH},s}}} \right)} \\ {k = 0,1,\ldots,M_{\text{sc}}^{\text{PUCCH},s} - 1} \\ {l = 0,1,\ldots,\left( {{N_{\text{SF}}^{\text{PUCCH},s}M_{\text{symb}}}/M_{\text{sc}}^{\text{PUCCH},s}} \right) - 1} \end{matrix}\]

where

-    for PUCCH format 3 with interlaced mapping, \(N_{\text{SF}}^{\text{PUCCH,}3} \in \left\{ {1,2,4} \right\}\) if a single interlace is configured and \(N_{\text{SF}}^{\text{PUCCH,}3} = 1\), \(w_{n} = 1\) if two interlaces are configured;

-    for PUCCH format 4,\(M_{\text{RB}}^{PUCCH,4}isgivenbyclause9.2.1of\left\lbrack 5,TS38.213 \right\rbrack\text{and}\) \(N_{\text{SF}}^{\text{PUCCH,}4} \in \left\{ 2,4 \right\}\) is given by the higher-layer parameter occ-Length;

and \(w_n\) is given by Tables 6.3.2.6.3-1 and 6.3.2.6.3-2 for \(N_{\text{SF}}^{\text{PUCCH,}s} > 1\) where \(n\) is the index of the orthogonal sequence to use according to clause 9.2.1 of [5, TS 38.213]. The quantity \(N_{\text{SF}}^{\text{PUCCH,}3} \in \left\{ 2,4 \right\}\) is given by the higher-layer parameter occ-Length if provided, otherwise \(N_{\text{SF}}^{\text{PUCCH,}3} = 1\).

Table 6.3.2.6.3-1: Orthogonal sequences \(w_n(m)\) for PUCCH format 3 with interlaced mapping and PUCCH format 4 when \(\mathbf{N}_{\text{SF}}^{\text{PUCCH,}\mathbf{s}} = 2\).

\(n\)

\(w_n\)

0

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

1

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

 

Table 6.3.2.6.3-2: Orthogonal sequences \(w_n(m)\) for PUCCH format 3 with interlaced mapping and PUCCH format 4 when \(\mathbf{N}_{\text{SF}}^{\text{PUCCH,}\mathbf{s}} = 4\).

\(n\)

\(w_n\)

0

\[\begin{bmatrix} {+ 1} & {+ 1} & {+ 1} & {+ 1} \end{bmatrix}\]

1

\[\begin{bmatrix} {+ 1} & {- j} & {- 1} & {+ j} \end{bmatrix}\]

2

\[\begin{bmatrix} {+ 1} & {- 1} & {+ 1} & {- 1} \end{bmatrix}\]

3

\[\begin{bmatrix} {+ 1} & {+ j} & {- 1} & {- j} \end{bmatrix}\]

 

6.3.2. 6.4    Transform precoding #

The block of complex-valued symbols \(y(0),\ldots,y\left( N_{\text{SF}}^{\text{PUCCH},s}M_{\text{symb}} - 1 \right)\) shall be transform precoded according to

\(\begin{aligned} z\!\left(l\cdot M_{sc}^{\mathrm{PUCCH},s}+k\right) &=\frac{1}{\sqrt{M_{sc}^{\mathrm{PUCCH},s}}}\sum_{m=0}^{M_{sc}^{\mathrm{PUCCH},s}-1} y\!\left(l\cdot M_{sc}^{\mathrm{PUCCH},s}+m\right) e^{-j\frac{2\pi mk}{M_{sc}^{\mathrm{PUCCH},s}}},\\ k&=0,\ldots,M_{sc}^{\mathrm{PUCCH},s}-1,\\ l&=0,\ldots,\left(\frac{N_{SF}^{\mathrm{PUCCH},s} M_{\mathrm{symb}}}{M_{sc}^{\mathrm{PUCCH},s}}\right)-1. \end{aligned}\)

resulting in a block of complex-valued symbols \(z(0),\ldots,z\left( N_{\text{SF}}^{\text{PUCCH},s}M_{\text{symb}} - 1 \right)\).

 

6.3.2. 6.5    Mapping to physical resources #

The block of modulation symbols \(z(0),\ldots,z\left( N_{\text{SF}}^{\text{PUCCH},s}M_{\text{symb}} - 1 \right)\) shall be multiplied with the amplitude scaling factor \(\beta_{\mathrm{PUCCH},s}\) in order to conform to the transmit power specified in [5, TS 38.213] and mapped in sequence starting with \(z(0)\) to resource elements \((k,l)_{p,\mu}\) which meet all of the following criteria:

-    they are in the resource blocks assigned for transmission,

-    they are not used by the associated DM-RS

The mapping to resource elements \((k,l)_{p,\mu}\) not reserved for other purposes shall be in increasing order of first the index \(k\) over the assigned physical resource blocks according to clause 9.2.1 of [5, TS 38.213], and then the index \(l\) on antenna port \(p=2000\).

In case of intra-slot frequency hopping according to clause 9.2.1 of [5, TS 38.213], \(\left\lfloor \frac{N_{\mathrm{symb}}^{\mathrm{PUCCH},s}}{2} \right\rfloor\) OFDM symbols shall be transmitted in the first hop and \(N_{\mathrm{symb}}^{\mathrm{PUCCH},s}-\left\lfloor\frac{N_{\mathrm{symb}}^{\mathrm{PUCCH},s}}{2}\right\rfloor\) symbols in the second hop where \(N^{\mathrm{PUCCH},s}_{\mathrm{symb}}\) is the total number of OFDM symbols used in one slot for PUCCH transmission.

6 .3.3    Physical random-access channel #

6.3.3.1     Sequence generation #

The set of random-access preambles \(x_{u,v}(n)\) shall be generated according to

\(\[ x_{u,v}(n)=x_u\big((n+C_v)\bmod L_{RA}\big) \] \[ x_u(i)=e^{-j\frac{\pi u\, i(i+1)}{L_{RA}}},\quad i=0,1,\ldots,L_{RA}-1 \]\)

from which the frequency-domain representation shall be generated according to

\(y_{u,v}(n)=\sum_{m=0}^{L_{RA}-1} x_{u,v}(m)\cdot e^{-j\frac{2\pi mn}{L_{RA}}}\)

where \(L_{RA}=839\), \(L_{RA}=139\), \(L_{\text{RA}} = 1151\), or \(L_{\text{RA}} = 571\) depending on the PRACH preamble format as given by Tables 6.3.3.1-1 and 6.3.3.1-2.

There are 64 preambles defined in each time-frequency PRACH occasion, enumerated in increasing order of first increasing cyclic shift \(C_{v}\) of a logical root sequence, and then in increasing order of the logical root sequence index, starting with the index obtained from the higher-layer parameter prach-RootSequenceIndex or rootSequenceIndex-BFR or by msgA-PRACH-RootSequenceIndex if configured and a type-2 random-access procedure is initiated as described in clause 8.1 of [5, TS 38.213] or by prach-RootSequenceIndex in EarlyUL-SyncConfig if the PRACH transmission is for a candidate cell. Additional preamble sequences, in case 64 preambles cannot be generated from a single root Zadoff-Chu sequence, are obtained from the root sequences with the consecutive logical indexes until all the 64 sequences are found. The logical root sequence order is cyclic; the logical index 0 is consecutive to \(L_{\text{RA}} - 2\). The sequence number \(\boldsymbol{u}\) is obtained from the logical root sequence index according to Tables 6.3.3.1-3 to 6.3.3.1-4B.

The cyclic shift \(C_{v}\) is given by

\(\[ C_v=\begin{cases} v N_{CS}, & v=0,1,\ldots,\left\lfloor \dfrac{L_{RA}}{N_{CS}} \right\rfloor-1,\; N_{CS}\neq 0 \ \text{for unrestricted sets},\\ 0, & N_{CS}=0 \ \text{for unrestricted sets},\\ \bar d_{\text{start}}\left\lfloor \dfrac{v}{n^{RA}_{\text{shift}}}\right\rfloor + \bigl(v \bmod n^{RA}_{\text{shift}}\bigr) N_{CS}, & v=0,1,\ldots,w-1 \ \text{for restricted sets type A and B},\\ \bar d_{\text{start}}+(v-w)N_{CS}, & v=w,\ldots,w+\bar n^{RA}_{\text{shift}}-1 \ \text{for restricted sets type B},\\ \bar d_{\text{start}}+(v-w-\bar n^{RA}_{\text{shift}})N_{CS}, & v=w+\bar n^{RA}_{\text{shift}},\ldots,w+\bar n^{RA}_{\text{shift}}+\bar n^{RA}_{\text{shift}}-1 \ \text{for restricted sets type B}. \end{cases} \] \[ w=n^{RA}_{\text{shift}}\,n^{RA}_{\text{group}}+\bar n^{RA}_{\text{shift}} \]\)

where \(N_{cs}\) is given by Tables 6.3.3.1-5 to 6.3.3.1-7. The type of restricted sets (unrestricted, restricted type A, restricted type B) is given by

-    the higher-layer parameter msgA-RestrictedSetConfig, if provided;

-    or the higher-layer parameter ltm-restrictedSetConfig associated with a candidate cell indicated in Cell indicator field of a PDCCH order, if provided;

-    otherwise, the higher-layer parameter restrictedSetConfig.

Tables 6.3.3.1-1 and 6.3.3.1-2 indicate the type of restricted sets supported for the different preamble formats.

The variable \(d_{u}\) is given by

\(\[ d_u = \begin{cases} q, & 0 \le q < \frac{L_{\mathrm{RA}}}{2} \\ L_{\mathrm{RA}} - q, & \text{otherwise} \end{cases} \]\)

where \(q\) is the smallest non-negative integer that fulfils \((qu)\bmod L_{RA} = 1\). The parameters for restricted sets of cyclic shifts depend on \(d_{u}\).

For restricted set type A, the parameters are given by:

-    for \(N_{CS} \le d_u < \frac{L_{RA}}{3}\)

\(n_{\mathrm{shift}}^{\mathrm{RA}}=\left\lfloor \frac{d_u}{N_{\mathrm{CS}}}\right\rfloor \\ d_{\mathrm{start}}=2d_u+n_{\mathrm{shift}}^{\mathrm{RA}}N_{\mathrm{CS}} \\ n_{\mathrm{group}}^{\mathrm{RA}}=\left\lfloor \frac{L_{\mathrm{RA}}}{d_{\mathrm{start}}}\right\rfloor \\ \bar{n}_{\mathrm{shift}}^{\mathrm{RA}}=\max\!\left(\left\lfloor \frac{L_{\mathrm{RA}}-2d_u-n_{\mathrm{group}}^{\mathrm{RA}}d_{\mathrm{start}}}{N_{\mathrm{CS}}}\right\rfloor,0\right)\)

-    for \(L_{RA}/3 \le d_u \le (L_{RA} - N_{CS})/2\)

\(\begin{aligned} n_{\text{shift}}^{\mathrm{RA}} &= \left\lfloor \frac{L_{\mathrm{RA}} - 2 d_u}{N_{\mathrm{CS}}} \right\rfloor \\ d_{\text{start}} &= L_{\mathrm{RA}} - 2 d_u + n_{\text{shift}}^{\mathrm{RA}} N_{\mathrm{CS}} \\ n_{\text{group}}^{\mathrm{RA}} &= \left\lfloor \frac{d_u}{d_{\text{start}}} \right\rfloor \\ \bar{n}_{\text{shift}}^{\mathrm{RA}} &= \min\!\left( \max\!\left( \left\lfloor \frac{ d_u - n_{\text{group}}^{\mathrm{RA}} d_{\text{start}} }{ N_{\mathrm{CS}} } \right\rfloor , 0 \right), n_{\text{shift}}^{\mathrm{RA}} \right) \end{aligned}\)

For restricted set type B, the parameters are given by:

-    for \(N_{\mathrm{CS}} \le d_u < \frac{L_{\mathrm{RA}}}{5}\)

\(\begin{aligned} n_{\text{shift}}^{\mathrm{RA}} &= \left\lfloor \frac{d_u}{N_{\mathrm{CS}}} \right\rfloor \\ d_{\text{start}} &= 4 d_u + n_{\text{shift}}^{\mathrm{RA}} N_{\mathrm{CS}} \\ n_{\text{group}}^{\mathrm{RA}} &= \left\lfloor \frac{L_{\mathrm{RA}}}{d_{\text{start}}} \right\rfloor \\ \bar{n}_{\text{shift}}^{\mathrm{RA}} &= \max\!\left( \left\lfloor \frac{L_{\mathrm{RA}} - 4 d_u - n_{\text{group}}^{\mathrm{RA}} d_{\text{start}}}{N_{\mathrm{CS}}} \right\rfloor ,\, 0 \right) \end{aligned}\)

-    for \(L_{\mathrm{RA}}/5 \le d_u \le (L_{\mathrm{RA}} - N_{\mathrm{CS}})/4\)

\(\begin{aligned} n_{\mathrm{shift}}^{\mathrm{RA}}&=\left\lfloor\frac{L_{\mathrm{RA}}-4d_u}{N_{\mathrm{CS}}}\right\rfloor\\ d_{\mathrm{start}}&=L_{\mathrm{RA}}-4d_u+n_{\mathrm{shift}}^{\mathrm{RA}}N_{\mathrm{CS}}\\ n_{\mathrm{group}}^{\mathrm{RA}}&=\left\lfloor\frac{d_u}{d_{\mathrm{start}}}\right\rfloor\\ \bar n_{\mathrm{shift}}^{\mathrm{RA}}&=\min\!\left(\max\!\left(\left\lfloor\frac{d_u-n_{\mathrm{group}}^{\mathrm{RA}}\,d_{\mathrm{start}}}{N_{\mathrm{CS}}}\right\rfloor,\,0\right),\,n_{\mathrm{shift}}^{\mathrm{RA}}\right) \end{aligned}\)

-    for \(\frac{L_{RA}+N_{CS}}{4} \le d_u < \frac{2L_{RA}}{7}\)

Image

-    for \(2L_{RA}/7 \le d_u \le (L_{RA}-N_{CS})/3\)

Image

-    for \((L_{RA}+N_{CS})/3\le d_u<2L_{RA}/5\)

\(\[ \begin{aligned} n_{\mathrm{shift}}^{\mathrm{RA}} &= \left\lfloor \frac{3 d_u - L_{\mathrm{RA}}}{N_{\mathrm{CS}}} \right\rfloor \\ d_{\mathrm{start}} &= 3 d_u - L_{\mathrm{RA}} + n_{\mathrm{shift}}^{\mathrm{RA}} N_{\mathrm{CS}} \\ \bar{d}_{\mathrm{start}} &= 0 \\ \bar{\bar{d}}_{\mathrm{start}} &= 0 \\ n_{\mathrm{group}}^{\mathrm{RA}} &= \left\lfloor \frac{d_u}{d_{\mathrm{start}}} \right\rfloor \\ \bar{n}_{\mathrm{shift}}^{\mathrm{RA}} &= \max\!\left( \left\lfloor \frac{L_{\mathrm{RA}} - 2 d_u - n_{\mathrm{group}}^{\mathrm{RA}} d_{\mathrm{start}}}{N_{\mathrm{CS}}} \right\rfloor ,\, 0 \right) \\ \bar{n}_{\mathrm{shift}}^{\mathrm{RA}} &= 0 \\ \bar{\bar{n}}_{\mathrm{shift}}^{\mathrm{RA}} &= 0 \end{aligned} \]\)

-    for \(\frac{2L_{RA}}{5} \le d_{u} \le \frac{L_{RA}-N_{CS}}{2}\)

Image

For all other values of \(d_{u}\), there are no cyclic shifts in the restricted set.

Table 6.3.3.1-1: PRACH preamble formats for \(L_{\mathrm{RA}} = 839\) and \(\mathbf{\Delta}\mathbf{f}_{\text{RA}} \in \left\{ {1.25,\mathbf{}5} \right\}\) kHz.

Format

\(L_{RA}\)

\[\mathbf{\Delta}\mathbf{f}_{\text{RA}}\]

\(N_{u}\)

\(N^{\mathrm{RA}}_{\mathrm{CP}}\)

Support for restricted sets

0

839

1.25 kHz

\[24576\kappa\]

\[3168\kappa\]

Type A, Type B

1

839

1.25 kHz

\[2 \cdot 24576\kappa\]

\[21024\kappa\]

Type A, Type B

2

839

1.25 kHz

\[4 \cdot 24576\kappa\]

\[4688\kappa\]

Type A, Type B

3

839

5 kHz

\[4 \cdot 6144\kappa\]

\[3168\kappa\]

Type A, Type B

 

Table 6.3.3.1-2: Preamble formats for \(\mathbf{L}_{\text{RA}} \in \left\{ {139,\mathbf{}571,\mathbf{}1151} \right\}\) and \(\mathbf{\Delta}\mathbf{f}_{\text{RA}} = 15 \cdot 2^{\mathbf{\mu}}\) kHz where \(\mathbf{\mu} \in \left\{ {0,1,2,3,5,6} \right\}\).

Format

\(L_{RA}\)

\[\mathbf{\Delta}\mathbf{f}_{\text{RA}}\]

\(N_{u}\)

\(N^{\mathrm{RA}}_{\mathrm{CP}}\)

Support for restricted sets

\[\mathbf{\mu} \in \left\{ {0,1,2,3,5,6} \right\}\]

\[\mathbf{\mu} \in \left\{ 0,3 \right\}\]

\[\mathbf{\mu} \in \left\{ {1,3,\mathbf{}5} \right\}\]

A1

139

1151

571

\(15\cdot 2^{\mu}\,\mathrm{kHz}\)

\(2\cdot 2048\kappa\cdot 2^{-\mu}\)

\(288\kappa\cdot 2^{-\mu}\)

-

A2

139

1151

571

\(15\cdot 2^{\mu}\,\mathrm{kHz}\)

\(4\cdot 2048\kappa \cdot 2^{-\mu}\)

\(576\kappa\cdot 2^{-\mu}\)

-

A3

139

1151

571

\(15\cdot 2^{\mu}\,\mathrm{kHz}\)

\(6\cdot 2048\kappa\cdot 2^{-\mu}\)

\(864\kappa\cdot 2^{-\mu}\)

-

B1

139

1151

571

\(15\cdot 2^{\mu}\,\mathrm{kHz}\)

\(2\cdot 2048\kappa\cdot 2^{-\mu}\)

\(216\kappa\cdot 2^{-\mu}\)

-

B2

139

1151

571

\(15\cdot 2^{\mu}\,\mathrm{kHz}\)

\(4\cdot 2048\kappa \cdot 2^{-\mu}\)

\(360\kappa \cdot 2^{-\mu}\)

-

B3

139

1151

571

\(15\cdot 2^{\mu}\,\mathrm{kHz}\)

\(6\cdot 2048\kappa\cdot 2^{-\mu}\)

\(504\kappa\cdot 2^{-\mu}\)

-

B4

139

1151

571

\(15\cdot 2^{\mu}\,\mathrm{kHz}\)

\(12\cdot 2048\kappa\cdot 2^{-\mu}\)

\(936\kappa\cdot 2^{-\mu}\)

-

C0

139

1151

571

\(15\cdot 2^{\mu}\,\mathrm{kHz}\)

\(2048\kappa\cdot 2^{-\mu}\)

\(1240\kappa\cdot 2^{-\mu}\)

-

C2

139

1151

571

\(15\cdot 2^{\mu}\,\mathrm{kHz}\)

\(4\cdot 2048\kappa \cdot 2^{-\mu}\)

\(2048\kappa\cdot 2^{-\mu}\)

 

 

Table 6.3.3.1-3: Mapping from logical index \(i\) to sequence number \(u\) for preamble formats with \(L_{\mathrm{RA}} = 839\).

\(i\)

Sequence number \(u\)in increasing order of \(i\)

0 – 19

129

710

140

699

120

719

210

629

168

671

84

755

105

734

93

746

70

769

60

779

20 – 39

2

837

1

838

56

783

112

727

148

691

80

759

42

797

40

799

35

804

73

766

40 – 59

146

693

31

808

28

811

30

809

27

812

29

810

24

815

48

791

68

771

74

765

60 – 79

178

661

136

703

86

753

78

761

43

796

39

800

20

819

21

818

95

744

202

637

80 – 99

190

649

181

658

137

702

125

714

151

688

217

622

128

711

142

697

122

717

203

636

100 – 119

118

721

110

729

89

750

103

736

61

778

55

784

15

824

14

825

12

827

23

816

120 – 139

34

805

37

802

46

793

207

632

179

660

145

694

130

709

223

616

228

611

227

612

140 – 159

132

707

133

706

143

696

135

704

161

678

201

638

173

666

106

733

83

756

91

748

160 – 179

66

773

53

786

10

829

9

830

7

832

8

831

16

823

47

792

64

775

57

782

180 – 199

104

735

101

738

108

731

208

631

184

655

197

642

191

648

121

718

141

698

149

690

200 – 219

216

623

218

621

152

687

144

695

134

705

138

701

199

640

162

677

176

663

119

720

220 – 239

158

681

164

675

174

665

171

668

170

669

87

752

169

670

88

751

107

732

81

758

240 – 259

82

757

100

739

98

741

71

768

59

780

65

774

50

789

49

790

26

813

17

822

260 – 279

13

826

6

833

5

834

33

806

51

788

75

764

99

740

96

743

97

742

166

673

280 – 299

172

667

175

664

187

652

163

676

185

654

200

639

114

725

189

650

115

724

194

645

300 – 319

195

644

192

647

182

657

157

682

156

683

211

628

154

685

123

716

139

700

212

627

320 – 339

153

686

213

626

215

624

150

689

225

614

224

615

221

618

220

619

127

712

147

692

340 – 359

124

715

193

646

205

634

206

633

116

723

160

679

186

653

167

672

79

760

85

754

360 – 379

77

762

92

747

58

781

62

777

69

770

54

785

36

803

32

807

25

814

18

821

380 – 399

11

828

4

835

3

836

19

820

22

817

41

798

38

801

44

795

52

787

45

794

400 – 419

63

776

67

772

72

767

76

763

94

745

102

737

90

749

109

730

165

674

111

728

420 – 439

209

630

204

635

117

722

188

651

159

680

198

641

113

726

183

656

180

659

177

662

440 – 459

196

643

155

684

214

625

126

713

131

708

219

620

222

617

226

613

230

609

232

607

460 – 479

262

577

252

587

418

421

416

423

413

426

411

428

376

463

395

444

283

556

285

554

480 – 499

379

460

390

449

363

476

384

455

388

451

386

453

361

478

387

452

360

479

310

529

500 – 519

354

485

328

511

315

524

337

502

349

490

335

504

324

515

323

516

320

519

334

505

520 – 539

359

480

295

544

385

454

292

547

291

548

381

458

399

440

380

459

397

442

369

470

540 – 559

377

462

410

429

407

432

281

558

414

425

247

592

277

562

271

568

272

567

264

575

560 – 579

259

580

237

602

239

600

244

595

243

596

275

564

278

561

250

589

246

593

417

422

580 – 599

248

591

394

445

393

446

370

469

365

474

300

539

299

540

364

475

362

477

298

541

600 – 619

312

527

313

526

314

525

353

486

352

487

343

496

327

512

350

489

326

513

319

520

620 – 639

332

507

333

506

348

491

347

492

322

517

330

509

338

501

341

498

340

499

342

497

640 – 659

301

538

366

473

401

438

371

468

408

431

375

464

249

590

269

570

238

601

234

605

660 – 679

257

582

273

566

255

584

254

585

245

594

251

588

412

427

372

467

282

557

403

436

680 – 699

396

443

392

447

391

448

382

457

389

450

294

545

297

542

311

528

344

495

345

494

700 – 719

318

521

331

508

325

514

321

518

346

493

339

500

351

488

306

533

289

550

400

439

720 – 739

378

461

374

465

415

424

270

569

241

598

231

608

260

579

268

571

276

563

409

430

740 – 759

398

441

290

549

304

535

308

531

358

481

316

523

293

546

288

551

284

555

368

471

760 – 779

253

586

256

583

263

576

242

597

274

565

402

437

383

456

357

482

329

510

317

522

780 – 799

307

532

286

553

287

552

266

573

261

578

236

603

303

536

356

483

355

484

405

434

800 – 819

404

435

406

433

235

604

267

572

302

537

309

530

265

574

233

606

367

472

296

543

820 – 837

336

503

305

534

373

466

280

559

279

560

419

420

240

599

258

581

229

610

-

-

 

Table 6.3.3.1-4: Mapping from logical index \(i\) to sequence number \(u\) for preamble formats with \(L_{RA} = 139\).

\(i\)

Sequence number \(u\) in increasing order of \(i\)

0 – 19

1

138

2

137

3

136

4

135

5

134

6

133

7

132

8

131

9

130

10

129

20 – 39

11

128

12

127

13

126

14

125

15

124

16

123

17

122

18

121

19

120

20

119

40 – 59

21

118

22

117

23

116

24

115

25

114

26

113

27

112

28

111

29

110

30

109

60 – 79

31

108

32

107

33

106

34

105

35

104

36

103

37

102

38

101

39

100

40

99

80 – 99

41

98

42

97

43

96

44

95

45

94

46

93

47

92

48

91

49

90

50

89

100 – 119

51

88

52

87

53

86

54

85

55

84

56

83

57

82

58

81

59

80

60

79

120 – 137

61

78

62

77

63

76

64

75

65

74

66

73

67

72

68

71

69

70

-

-

138 – 837

N/A

 

Table 6.3.3.1-4A: Mapping from logical index \(\mathbf{i}\) to sequence number \(\mathbf{u}\) for preamble formats with \(\mathbf{L}_{\text{RA}} = 1151\).

\[\mathbf{i}\]

Sequence number \(\mathbf{u}\) in increasing order of \(\mathbf{i}\)

0-19

1

1150

2

1149

3

1148

4

1147

5

1146

6

1145

7

1144

8

1143

9

1142

10

1141

20-39

11

1140

12

1139

13

1138

14

1137

15

1136

16

1135

17

1134

18

1133

19

1132

20

1131

40-59

21

1130

22

1129

23

1128

24

1127

25

1126

26

1125

27

1124

28

1123

29

1122

30

1121

60-79

31

1120

32

1119

33

1118

34

1117

35

1116

36

1115

37

1114

38

1113

39

1112

40

1111

80-99

41

1110

42

1109

43

1108

44

1107

45

1106

46

1105

47

1104

48

1103

49

1102

50

1101

100-119

51

1100

52

1099

53

1098

54

1097

55

1096

56

1095

57

1094

58

1093

59

1092

60

1091

120-139

61

1090

62

1089

63

1088

64

1087

65

1086

66

1085

67

1084

68

1083

69

1082

70

1081

140-159

71

1080

72

1079

73

1078

74

1077

75

1076

76

1075

77

1074

78

1073

79

1072

80

1071

160-179

81

1070

82

1069

83

1068

84

1067

85

1066

86

1065

87

1064

88

1063

89

1062

90

1061

180-199

91

1060

92

1059

93

1058

94

1057

95

1056

96

1055

97

1054

98

1053

99

1052

100

1051

200-219

101

1050

102

1049

103

1048

104

1047

105

1046

106

1045

107

1044

108

1043

109

1042

110

1041

220-239

111

1040

112

1039

113

1038

114

1037

115

1036

116

1035

117

1034

118

1033

119

1032

120

1031

240-259

121

1030

122

1029

123

1028

124

1027

125

1026

126

1025

127

1024

128

1023

129

1022

130

1021

260-279

131

1020

132

1019

133

1018

134

1017

135

1016

136

1015

137

1014

138

1013

139

1012

140

1011

280-299

141

1010

142

1009

143

1008

144

1007

145

1006

146

1005

147

1004

148

1003

149

1002

150

1001

300-319

151

1000

152

999

153

998

154

997

155

996

156

995

157

994

158

993

159

992

160

991

320-339

161

990

162

989

163

988

164

987

165

986

166

985

167

984

168

983

169

982

170

981

340-359

171

980

172

979

173

978

174

977

175

976

176

975

177

974

178

973

179

972

180

971

360-379

181

970

182

969

183

968

184

967

185

966

186

965

187

964

188

963

189

962

190

961

380-399

191

960

192

959

193

958

194

957

195

956

196

955

197

954

198

953

199

952

200

951

400-419

201

950

202

949

203

948

204

947

205

946

206

945

207

944

208

943

209

942

210

941

420-439

211

940

212

939

213

938

214

937

215

936

216

935

217

934

218

933

219

932

220

931

440-459

221

930

222

929

223

928

224

927

225

926

226

925

227

924

228

923

229

922

230

921

460-479

231

920

232

919

233

918

234

917

235

916

236

915

237

914

238

913

239

912

240

911

480-499

241

910

242

909

243

908

244

907

245

906

246

905

247

904

248

903

249

902

250

901

500-519

251

900

252

899

253

898

254

897

255

896

256

895

257

894

258

893

259

892

260

891

520-539

261

890

262

889

263

888

264

887

265

886

266

885

267

884

268

883

269

882

270

881

540-559

271

880

272

879

273

878

274

877

275

876

276

875

277

874

278

873

279

872

280

871

560-579

281

870

282

869

283

868

284

867

285

866

286

865

287

864

288

863

289

862

290

861

580-599

291

860

292

859

293

858

294

857

295

856

296

855

297

854

298

853

299

852

300

851

600-619

301

850

302

849

303

848

304

847

305

846

306

845

307

844

308

843

309

842

310

841

620-639

311

840

312

839

313

838

314

837

315

836

316

835

317

834

318

833

319

832

320

831

640-659

321

830

322

829

323

828

324

827

325

826

326

825

327

824

328

823

329

822

330

821

660-679

331

820

332

819

333

818

334

817

335

816

336

815

337

814

338

813

339

812

340

811

680-699

341

810

342

809

343

808

344

807

345

806

346

805

347

804

348

803

349

802

350

801

700-719

351

800

352

799

353

798

354

797

355

796

356

795

357

794

358

793

359

792

360

791

720-739

361

790

362

789

363

788

364

787

365

786

366

785

367

784

368

783

369

782

370

781

740-759

371

780

372

779

373

778

374

777

375

776

376

775

377

774

378

773

379

772

380

771

760-779

381

770

382

769

383

768

384

767

385

766

386

765

387

764

388

763

389

762

390

761

780-799

391

760

392

759

393

758

394

757

395

756

396

755

397

754

398

753

399

752

400

751

800-819

401

750

402

749

403

748

404

747

405

746

406

745

407

744

408

743

409

742

410

741

820-839

411

740

412

739

413

738

414

737

415

736

416

735

417

734

418

733

419

732

420

731

840-859

421

730

422

729

423

728

424

727

425

726

426

725

427

724

428

723

429

722

430

721

860-879

431

720

432

719

433

718

434

717

435

716

436

715

437

714

438

713

439

712

440

711

880-899

441

710

442

709

443

708

444

707

445

706

446

705

447

704

448

703

449

702

450

701

900-919

451

700

452

699

453

698

454

697

455

696

456

695

457

694

458

693

459

692

460

691

920-939

461

690

462

689

463

688

464

687

465

686

466

685

467

684

468

683

469

682

470

681

940-959

471

680

472

679

473

678

474

677

475

676

476

675

477

674

478

673

479

672

480

671

960-979

481

670

482

669

483

668

484

667

485

666

486

665

487

664

488

663

489

662

490

661

980-999

491

660

492

659

493

658

494

657

495

656

496

655

497

654

498

653

499

652

500

651

1000-1019

501

650

502

649

503

648

504

647

505

646

506

645

507

644

508

643

509

642

510

641

1020-1039

511

640

512

639

513

638

514

637

515

636

516

635

517

634

518

633

519

632

520

631

1040-1059

521

630

522

629

523

628

524

627

525

626

526

625

527

624

528

623

529

622

530

621

1060-1079

531

620

532

619

533

618

534

617

535

616

536

615

537

614

538

613

539

612

540

611

1080-1099

541

610

542

609

543

608

544

607

545

606

546

605

547

604

548

603

549

602

550

601

1100-1119

551

600

552

599

553

598

554

597

555

596

556

595

557

594

558

593

559

592

560

591

1120-1139

561

590

562

589

563

588

564

587

565

586

566

585

567

584

568

583

569

582

570

581

1140-1149

571

580

572

579

573

578

574

577

575

576

-

-

-

-

-

-

-

-

-

-

 

Table 6.3.3.1-4B: Mapping from logical index \(\mathbf{i}\) to sequence number \(\mathbf{u}\) for preamble formats with \(\mathbf{L}_{\text{RA}} = 571\).

\[\mathbf{i}\]

Sequence number \(\mathbf{u}\) in increasing order of \(\mathbf{i}\)

0-19

1

570

2

569

3

568

4

567

5

566

6

565

7

564

8

563

9

562

10

561

20-39

11

560

12

559

13

558

14

557

15

556

16

555

17

554

18

553

19

552

20

551

40-59

21

550

22

549

23

548

24

547

25

546

26

545

27

544

28

543

29

542

30

541

60-79

31

540

32

539

33

538

34

537

35

536

36

535

37

534

38

533

39

532

40

531

80-99

41

530

42

529

43

528

44

527

45

526

46

525

47

524

48

523

49

522

50

521

100-119

51

520

52

519

53

518

54

517

55

516

56

515

57

514

58

513

59

512

60

511

120-139

61

510

62

509

63

508

64

507

65

506

66

505

67

504

68

503

69

502

70

501

140-159

71

500

72

499

73

498

74

497

75

496

76

495

77

494

78

493

79

492

80

491

160-179

81

490

82

489

83

488

84

487

85

486

86

485

87

484

88

483

89

482

90

481

180-199

91

480

92

479

93

478

94

477

95

476

96

475

97

474

98

473

99

472

100

471

200-219

101

470

102

469

103

468

104

467

105

466

106

465

107

464

108

463

109

462

110

461

220-239

111

460

112

459

113

458

114

457

115

456

116

455

117

454

118

453

119

452

120

451

240-259

121

450

122

449

123

448

124

447

125

446

126

445

127

444

128

443

129

442

130

441

260-279

131

440

132

439

133

438

134

437

135

436

136

435

137

434

138

433

139

432

140

431

280-299

141

430

142

429

143

428

144

427

145

426

146

425

147

424

148

423

149

422

150

421

300-319

151

420

152

419

153

418

154

417

155

416

156

415

157

414

158

413

159

412

160

411

320-339

161

410

162

409

163

408

164

407

165

406

166

405

167

404

168

403

169

402

170

401

340-359

171

400

172

399

173

398

174

397

175

396

176

395

177

394

178

393

179

392

180

391

360-379

181

390

182

389

183

388

184

387

185

386

186

385

187

384

188

383

189

382

190

381

380-399

191

380

192

379

193

378

194

377

195

376

196

375

197

374

198

373

199

372

200

371

400-419

201

370

202

369

203

368

204

367

205

366

206

365

207

364

208

363

209

362

210

361

420-439

211

360

212

359

213

358

214

357

215

356

216

355

217

354

218

353

219

352

220

351

440-459

221

350

222

349

223

348

224

347

225

346

226

345

227

344

228

343

229

342

230

341

460-479

231

340

232

339

233

338

234

337

235

336

236

335

237

334

238

333

239

332

240

331

480-499

241

330

242

329

243

328

244

327

245

326

246

325

247

324

248

323

249

322

250

321

500-519

251

320

252

319

253

318

254

317

255

316

256

315

257

314

258

313

259

312

260

311

520-539

261

310

262

309

263

308

264

307

265

306

266

305

267

304

268

303

269

302

270

301

540-559

271

300

272

299

273

298

274

297

275

296

276

295

277

294

278

293

279

292

280

291

560-569

281

290

282

289

283

288

284

287

285

286

-

-

-

-

-

-

-

-

-

-

 

Table 6.3.3.1-5: \(N_{cs}\) for preamble formats with \(\mathbf{\Delta}\mathbf{f}_{\text{RA}} = 1.25\) kHz.

zeroCorrelationZoneConfig, msgA-ZeroCorrelationZoneConfig<br>

\(N_{cs}\) value

Unrestricted set

Restricted set type A

Restricted set type B

0

0

15

15

1

13

18

18

2

15

22

22

3

18

26

26

4

22

32

32

5

26

38

38

6

32

46

46

7

38

55

55

8

46

68

68

9

59

82

82

10

76

100

100

11

93

128

118

12

119

158

137

13

167

202

-

14

279

237

-

15

419

-

-

 

Table 6.3.3.1-6: \(N_{cs}\) for preamble formats with \(\mathbf{\Delta}\mathbf{f}_{\text{RA}} = 5\) kHz.

zeroCorrelationZoneConfig, msgA-ZeroCorrelationZoneConfig<br>

\(N_{cs}\) value

Unrestricted set

Restricted set type A

Restricted set type B

0

0

36

36

1

13

57

57

2

26

72

60

3

33

81

63

4

38

89

65

5

41

94

68

6

49

103

71

7

55

112

77

8

64

121

81

9

76

132

85

10

93

137

97

11

119

152

109

12

139

173

122

13

209

195

137

14

279

216

-

15

419

237

-

 

Table 6.3.3.1-7: \(N_{cs}\) for preamble formats with \(\mathbf{L}_{\text{RA}} \in \left\{ {139,\mathbf{}571,\mathbf{}1151} \right\}\).

zeroCorrelationZoneConfig, msgA-ZeroCorrelationZoneConfig<br>

\(\mathbf{N}_{\text{CS}}\) value

 

\[\mathbf{L}_{\text{RA}} = 139\]

\[\mathbf{L}_{\text{RA}} = 571\]

\[\mathbf{L}_{\text{RA}} = 1151\]

0

0

0

0

1

2

8

17

2

4

10

21

3

6

12

25

4

8

15

30

5

10

17

35

6

12

21

44

7

13

25

52

8

15

31

63

9

17

40

82

10

19

51

104

11

23

63

127

12

27

81

164

13

34

114

230

14

46

190

383

15

69

285

575

 

6.3.3.2     Mapping to physical resources #

The preamble sequence shall be mapped to physical resources according to

\(\begin{aligned} a_k^{(p,\mathrm{RA})} &= \beta_{\mathrm{PRACH}} y_{u,v}(k) \\ k &= 0,1,\ldots,L_{\mathrm{RA}}-1 \end{aligned}\)

where \(\beta_{\mathrm{PRACH}}\) is an amplitude scaling factor in order to conform to the transmit power specified in [5, TS38.213], and \(\[p=4000\]\) is the antenna port. Baseband signal generation shall be done according to clause 5.3 using the parameters in Table 6.3.3.1-1 or Table 6.3.3.1-2 with \(\bar{k}\) given by Table 6.3.3.2-1.

Random access preambles can only be transmitted in the time resources obtained from Tables 6.3.3.2-2 to 6.3.3.2-4 and depends on FR1, FR2, or FR2-NTN and the spectrum type as defined in [8, TS38.104] or [17, TS38.108]. The PRACH configuration index in Tables 6.3.3.2-2 to 6.3.3.2-4 is

-    for Table 6.3.3.2-3 given by the higher-layer parameter prach-ConfigurationIndex, or by msgA-PRACH-ConfigurationIndex if configured; and

-    for Tables 6.3.3.2-2 and 6.3.3.2-4 given by the higher-layer parameter prach-ConfigurationIndex, or by msgA-PRACH-ConfigurationIndex if configured.

For the IAB-MT part of an IAB-node, the following applies:

-    if the higher-layer parameter prach-ConfigurationPeriodScaling-IAB is configured, the variable \(x\) used in \(n_{\text{f}}\text{mod}x = y\) of Tables 6.3.3.2-2 to 6.3.3.2-4 shall be replaced by \(x_{\text{IAB}}\) , where \(x_{\text{IAB}} = \delta x\) and \(\delta\) is given by the higher-layer parameter prach-ConfigurationPeriodScaling-IAB and the IAB-node does not expect \(x_{\text{IAB}}\) to be larger than 64;

-    if the higher-layer parameter prach-ConfigurationFrameOffset-IAB is configured, the variable \(y\) used in \(n_{f}\text{mod}x = y\) of Tables 6.3.3.2-2 to 6.3.3.2-4 shall be replaced by \(y_{\text{IAB}} = \left( {y + \Delta y} \right)\text{mod}x\) where \(\Delta y\) is given by the higher-layer parameter prach-ConfigurationFrameOffset-IAB, and \(xisthevalueused\text{in}n_{f}\text{mod}x = y\);

-    if the higher-layer parameter prach-ConfigurationSOffset-IAB is configured, the subframe number \(s_{\text{n}}\) from Tables 6.3.3.2-2 to 6.3.3.2-3 and the slot number \(s_{\text{n}}\) from Table 6.3.3.2-4 shall be replaced by \(\left( {s_{\text{n}} + \Delta s} \right)\text{mod}L\) where \(\Delta s \in \left\{ {0,1,\ldots,L - 1} \right\}\) is given by the higher-layer parameter prach-ConfigurationSOffset-IAB, and \(L\) is the number of subframes in a frame when using Tables 6.3.3.2-2 to 6.3.3.2-3 and the number of slots in a frame for 60 kHz subcarrier spacing when using in Table 6.3.3.2-4.

Random access preambles can only be transmitted in the frequency resources given by either the higher-layer parameter msg1-FrequencyStart or msgA-RO-FrequencyStart if configured as described in clause 8.1 of [5 TS 38.213]. The PRACH frequency resources \(n_{\text{RA}} \in \left\{ {0,1,\ldots,M - 1} \right\}\), where \(M\) equals the higher-layer parameter msg1-FDM or msgA-RO-FDM if configured, are numbered in increasing order within the initial uplink bandwidth part during initial access, starting from the lowest frequency. Otherwise, \(n_{\text{RA}}\) are numbered in increasing order within the active uplink bandwidth part, starting from the lowest frequency.

For operation with shared spectrum channel access, for \(L_{RA} = 139\), a UE expects to be provided with higher-layer parameter msg1-FrequencyStart or msgA-RO-FrequencyStart if configured, and higher-layer parameter msg1-FDM or msgA-RO-FDM if configured, such that a random-access preamble is confined within a single RB set. The UE assumes that the RB set is defined as when the UE is not provided intraCellGuardBandsPerSCS for an UL carrier as described in Clause 7 of [6, TS 38.214].

For operation with shared spectrum channel access, for \(L_{RA} = 571\) or \(1151\) and Type-2 random access, a UE expects to be provided with higher-layer parameter msgA-RO-FDM equals to one.

For the purpose of slot numbering in the tables, the following subcarrier spacing shall be assumed:

-    15 kHz for FR1

-    60 kHz for FR2 and FR2-NTN.

For handover purposes to a target cell in paired or unpaired spectrum where the target cell uses \(L_{\max} = 4\), the UE may assume the absolute value of the time difference between radio frame \(i\) in the current cell and radio frame \(i\) in the target cell is less than \(153600T_{\text{s}}\) if the association pattern period in clause 8.1 of [5, TS 38.213] is not equal to 10 ms.

For inter frequency handover purposes where the source cell is either in paired or unpaired spectrum and the target cell is in unpaired spectrum and uses \(L_{\max} = 8\), the UE may assume the absolute value of the time difference between radio frame \(i\) in the current cell and radio frame \(i\) in the target cell is less than \(76800T_{s}.\)

Table 6.3.3.2-1: Supported combinations of \(\mathbf{\Delta}\mathbf{f}_{\text{RA}}\) and \(\mathbf{\Delta}\mathbf{f}\), and the corresponding value of \(\bar{\mathbf{k}}\).

\(L_{RA}\)

\(\mathbf{\Delta}\mathbf{f}_{\text{RA}}\) for PRACH

\(\Delta f\) for PUSCH

\(N_{RB}^{RA}\), allocation expressed in number of RBs for PUSCH

\(\bar{k}\)

839

1.25

15

6

7

839

1.25

30

3

1

839

1.25

60

2

133

839

5

15

24

12

839

5

30

12

10

839

5

60

6

7

139

15

15

12

2

139

15

30

6

2

139

15

60

3

2

139

30

15

24

2

139

30

30

12

2

139

30

60

6

2

139

60

60

12

2

139

60

120

6

2

139

120

60

24

2

139

120

120

12

2

139

120

480

3

1

139

120

960

2

23

139

480

120

48

2

139

480

480

12

2

139

480

960

6

2

139

960

120

96

2

139

960

480

24

2

139

960

960

12

2

571

30

15

96

2

571

30

30

48

2

571

30

60

24

2

571

120

120

48

2

571

120

480

12

1

571

120

960

7

47

571

480

120

192

2

571

480

480

48

2

571

480

960

24

2

1151

15

15

96

1

1151

15

30

48

1

1151

15

60

24

1

1151

120

120

97

6

1151

120

480

25

23

1151

120

960

13

45

 

Table 6.3.3.2-2: Random access configurations for FR1 and paired spectrum/supplementary uplink.

PRACHConfiguration <br>Index<br>

Preamble format

\[\mathbf{n}_{\text{f}}\text{mod}\mathbf{x} = \mathbf{y}\]

Subframe number

Starting symbol

Number of PRACH slots within a subframe

\(N_{t}^{\mathrm{RA,slot}}\), number of time-domain PRACH occasions within a PRACH slot

\(N^{\mathrm{RA}}_{\mathrm{dur}}\),PRACH duration<br>

\(x\)

\(y\)

0

0

16

1

1

0

-

-

0

1

0

16

1

4

0

-

-

0

2

0

16

1

7

0

-

-

0

3

0

16

1

9

0

-

-

0

4

0

8

1

1

0

-

-

0

5

0

8

1

4

0

-

-

0

6

0

8

1

7

0

-

-

0

7

0

8

1

9

0

-

-

0

8

0

4

1

1

0

-

-

0

9

0

4

1

4

0

-

-

0

10

0

4

1

7

0

-

-

0

11

0

4

1

9

0

-

-

0

12

0

2

1

1

0

-

-

0

13

0

2

1

4

0

-

-

0

14

0

2

1

7

0

-

-

0

15

0

2

1

9

0

-

-

0

16

0

1

0

1

0

-

-

0

17

0

1

0

4

0

-

-

0

18

0

1

0

7

0

-

-

0

19

0

1

0

1,6

0

-

-

0

20

0

1

0

2,7

0

-

-

0

21

0

1

0

3,8

0

-

-

0

22

0

1

0

1,4,7

0

-

-

0

23

0

1

0

2,5,8

0

-

-

0

24

0

1

0

3, 6, 9

0

-

-

0

25

0

1

0

0,2,4,6,8

0

-

-

0

26

0

1

0

1,3,5,7,9

0

-

-

0

27

0

1

0

0,1,2,3,4,5,6,7,8,9

0

-

-

0

28

1

16

1

1

0

-

-

0

29

1

16

1

4

0

-

-

0

30

1

16

1

7

0

-

-

0

31

1

16

1

9

0

-

-

0

32

1

8

1

1

0

-

-

0

33

1

8

1

4

0

-

-

0

34

1

8

1

7

0

-

-

0

35

1

8

1

9

0

-

-

0

36

1

4

1

1

0

-

-

0

37

1

4

1

4

0

-

-

0

38

1

4

1

7

0

-

-

0

39

1

4

1

9

0

-

-

0

40

1

2

1

1

0

-

-

0

41

1

2

1

4

0

-

-

0

42

1

2

1

7

0

-

-

0

43

1

2

1

9

0

-

-

0

44

1

1

0

1

0

-

-

0

45

1

1

0

4

0

-

-

0

46

1

1

0

7

0

-

-

0

47

1

1

0

1,6

0

-

-

0

48

1

1

0

2,7

0

-

-

0

49

1

1

0

3,8

0

-

-

0

50

1

1

0

1,4,7

0

-

-

0

51

1

1

0

2,5,8

0

-

-

0

52

1

1

0

3,6,9

0

-

-

0

53

2

16

1

1

0

-

-

0

54

2

8

1

1

0

-

-

0

55

2

4

0

1

0

-

-

0

56

2

2

0

1

0

-

-

0

57

2

2

0

5

0

-

-

0

58

2

1

0

1

0

-

-

0

59

2

1

0

5

0

-

-

0

60

3

16

1

1

0

-

-

0

61

3

16

1

4

0

-

-

0

62

3

16

1

7

0

-

-

0

63

3

16

1

9

0

-

-

0

64

3

8

1

1

0

-

-

0

65

3

8

1

4

0

-

-

0

66

3

8

1

7

0

-

-

0

67

3

4

1

1

0

-

-

0

68

3

4

1

4

0

-

-

0

69

3

4

1

7

0

-

-

0

70

3

4

1

9

0

-

-

0

71

3

2

1

1

0

-

-

0

72

3

2

1

4

0

-

-

0

73

3

2

1

7

0

-

-

0

74

3

2

1

9

0

-

-

0

75

3

1

0

1

0

-

-

0

76

3

1

0

4

0

-

-

0

77

3

1

0

7

0

-

-

0

78

3

1

0

1,6

0

-

-

0

79

3

1

0

2,7

0

-

-

0

80

3

1

0

3,8

0

-

-

0

81

3

1

0

1,4,7

0

-

-

0

82

3

1

0

2,5,8

0

-

-

0

83

3

1

0

3, 6, 9

0

-

-

0

84

3

1

0

0,2,4,6,8

0

-

-

0

85

3

1

0

1,3,5,7,9

0

-

-

0

86

3

1

0

0,1,2,3,4,5,6,7,8,9

0

-

-

0

87

A1

16

0

4,9

0

1

6

2

88

A1

16

1

4

0

2

6

2

89

A1

8

0

4,9

0

1

6

2

90

A1

8

1

4

0

2

6

2

91

A1

4

0

4,9

0

1

6

2

92

A1

4

1

4,9

0

1

6

2

93

A1

4

0

4

0

2

6

2

94

A1

2

0

4,9

0

1

6

2

95

A1

2

0

1

0

2

6

2

96

A1

2

0

4

0

2

6

2

97

A1

2

0

7

0

2

6

2

98

A1

1

0

4

0

1

6

2

99

A1

1

0

1,6

0

1

6

2

100

A1

1

0

4,9

0

1

6

2

101

A1

1

0

1

0

2

6

2

102

A1

1

0

7

0

2

6

2

103

A1

1

0

2,7

0

2

6

2

104

A1

1

0

1,4,7

0

2

6

2

105

A1

1

0

0,2,4,6,8

0

2

6

2

106

A1

1

0

0,1,2,3,4,5,6,7,8,9

0

2

6

2

107

A1

1

0

1,3,5,7,9

0

2

6

2

108

A1/B1

2

0

4,9

0

1

7

2

109

A1/B1

2

0

4

0

2

7

2

110

A1/B1

1

0

4

0

1

7

2

111

A1/B1

1

0

1,6

0

1

7

2

112

A1/B1

1

0

4,9

0

1

7

2

113

A1/B1

1

0

1

0

2

7

2

114

A1/B1

1

0

7

0

2

7

2

115

A1/B1

1

0

1,4,7

0

2

7

2

116

A1/B1

1

0

0,2,4,6,8

0

2

7

2

117

A2

16

1

2,6,9

0

1

3

4

118

A2

16

1

4

0

2

3

4

119

A2

8

1

2,6,9

0

1

3

4

120

A2

8

1

4

0

2

3

4

121

A2

4

0

2,6,9

0

1

3

4

122

A2

4

0

4

0

2

3

4

123

A2

2

1

2,6,9

0

1

3

4

124

A2

2

0

1

0

2

3

4

125

A2

2

0

4

0

2

3

4

126

A2

2

0

7

0

2

3

4

127

A2

1

0

4

0

1

3

4

128

A2

1

0

1,6

0

1

3

4

129

A2

1

0

4,9

0

1

3

4

130

A2

1

0

1

0

2

3

4

131

A2

1

0

7

0

2

3

4

132

A2

1

0

2,7

0

2

3

4

133

A2

1

0

1,4,7

0

2

3

4

134

A2

1

0

0,2,4,6,8

0

2

3

4

135

A2

1

0

0,1,2,3,4,5,6,7,8,9

0

2

3

4

136

A2

1

0

1,3,5,7,9

0

2

3

4

137

A2/B2

2

1

2,6,9

0

1

3

4

138

A2/B2

2

0

4

0

2

3

4

139

A2/B2

1

0

4

0

1

3

4

140

A2/B2

1

0

1,6

0

1

3

4

141

A2/B2

1

0

4,9

0

1

3

4

142

A2/B2

1

0

1

0

2

3

4

143

A2/B2

1

0

7

0

2

3

4

144

A2/B2

1

0

1,4,7

0

2

3

4

145

A2/B2

1

0

0,2,4,6,8

0

2

3

4

146

A2/B2

1

0

0,1,2,3,4,5,6,7,8,9

0

2

3

4

147

A3

16

1

4,9

0

1

2

6

148

A3

16

1

4

0

2

2

6

149

A3

8

1

4,9

0

1

2

6

150

A3

8

1

4

0

2

2

6

151

A3

4

0

4,9

0

1

2

6

152

A3

4

0

4

0

2

2

6

153

A3

2

1

2,6,9

0

2

2

6

154

A3

2

0

1

0

2

2

6

155

A3

2

0

4

0

2

2

6

156

A3

2

0

7

0

2

2

6

157

A3

1

0

4

0

1

2

6

158

A3

1

0

1,6

0

1

2

6

159

A3

1

0

4,9

0

1

2

6

160

A3

1

0

1

0

2

2

6

161

A3

1

0

7

0

2

2

6

162

A3

1

0

2,7

0

2

2

6

163

A3

1

0

1,4,7

0

2

2

6

164

A3

1

0

0,2,4,6,8

0

2

2

6

165

A3

1

0

0,1,2,3,4,5,6,7,8,9

0

2

2

6

166

A3

1

0

1,3,5,7,9

0

2

2

6

167

A3/B3

2

1

2,6,9

0

2

2

6

168

A3/B3

2

0

4

0

2

2

6

169

A3/B3

1

0

4

0

1

2

6

170

A3/B3

1

0

1,6

0

1

2

6

171

A3/B3

1

0

4,9

0

1

2

6

172

A3/B3

1

0

1

0

2

2

6

173

A3/B3

1

0

7

0

2

2

6

174

A3/B3

1

0

1,4,7

0

2

2

6

175

A3/B3

1

0

0,2,4,6,8

0

2

2

6

176

A3/B3

1

0

0,1,2,3,4,5,6,7,8,9

0

2

2

6

177

B1

16

0

4,9

0

1

7

2

178

B1

16

1

4

0

2

7

2

179

B1

8

0

4,9

0

1

7

2

180

B1

8

1

4

0

2

7

2

181

B1

4

0

4,9

0

1

7

2

182

B1

4

1

4,9

0

1

7

2

183

B1

4

0

4

0

2

7

2

184

B1

2

0

4,9

0

1

7

2

185

B1

2

0

1

0

2

7

2

186

B1

2

0

4

0

2

7

2

187

B1

2

0

7

0

2

7

2

188

B1

1

0

4

0

1

7

2

189

B1

1

0

1,6

0

1

7

2

190

B1

1

0

4,9

0

1

7

2

191

B1

1

0

1

0

2

7

2

192

B1

1

0

7

0

2

7

2

193

B1

1

0

2,7

0

2

7

2

194

B1

1

0

1,4,7

0

2

7

2

195

B1

1

0

0,2,4,6,8

0

2

7

2

196

B1

1

0

0,1,2,3,4,5,6,7,8,9

0

2

7

2

197

B1

1

0

1,3,5,7,9

0

2

7

2

198

B4

16

0

4,9

0

2

1

12

199

B4

16

1

4

0

2

1

12

200

B4

8

0

4,9

0

2

1

12

201

B4

8

1

4

0

2

1

12

202

B4

4

0

4,9

0

2

1

12

203

B4

4

0

4

0

2

1

12

204

B4

4

1

4,9

0

2

1

12

205

B4

2

0

4,9

0

2

1

12

206

B4

2

0

1

0

2

1

12

207

B4

2

0

4

0

2

1

12

208

B4

2

0

7

0

2

1

12

209

B4

1

0

1

0

2

1

12

210

B4

1

0

4

0

2

1

12

211

B4

1

0

7

0

2

1

12

212

B4

1

0

1,6

0

2

1

12

213

B4

1

0

2,7

0

2

1

12

214

B4

1

0

4,9

0

2

1

12

215

B4

1

0

1,4,7

0

2

1

12

216

B4

1

0

0,2,4,6,8

0

2

1

12

217

B4

1

0

0,1,2,3,4,5,6,7,8,9

0

2

1

12

218

B4

1

0

1,3,5,7,9

0

2

1

12

219

C0

8

1

4

0

2

7

2

220

C0

4

1

4,9

0

1

7

2

221

C0

4

0

4

0

2

7

2

222

C0

2

0

4,9

0

1

7

2

223

C0

2

0

1

0

2

7

2

224

C0

2

0

4

0

2

7

2

225

C0

2

0

7

0

2

7

2

226

C0

1

0

4

0

1

7

2

227

C0

1

0

1,6

0

1

7

2

228

C0

1

0

4,9

0

1

7

2

229

C0

1

0

1

0

2

7

2

230

C0

1

0

7

0

2

7

2

231

C0

1

0

2,7

0

2

7

2

232

C0

1

0

1,4,7

0

2

7

2

233

C0

1

0

0,2,4,6,8

0

2

7

2

234

C0

1

0

0,1,2,3,4,5,6,7,8,9

0

2

7

2

235

C0

1

0

1,3,5,7,9

0

2

7

2

236

C2

16

1

4,9

0

1

2

6

237

C2

16

1

4

0

2

2

6

238

C2

8

1

4,9

0

1

2

6

239

C2

8

1

4

0

2

2

6

240

C2

4

0

4,9

0

1

2

6

241

C2

4

0

4

0

2

2

6

242

C2

2

1

2,6,9

0

2

2

6

243

C2

2

0

1

0

2

2

6

244

C2

2

0

4

0

2

2

6

245

C2

2

0

7

0

2

2

6

246

C2

1

0

4

0

1

2

6

247

C2

1

0

1,6

0

1

2

6

248

C2

1

0

4,9

0

1

2

6

249

C2

1

0

1

0

2

2

6

250

C2

1

0

7

0

2

2

6

251

C2

1

0

2,7

0

2

2

6

252

C2

1

0

1,4,7

0

2

2

6

253

C2

1

0

0,2,4,6,8

0

2

2

6

254

C2

1

0

0,1,2,3,4,5,6,7,8,9

0

2

2

6

255

C2

1

0

1,3,5,7,9

0

2

2

6

 

Table 6.3.3.2-3: Random access configurations for FR1 and unpaired spectrum.

PRACHConfiguration <br>Index<br>

Preamble format

\[\mathbf{n}_{\text{f}}\text{mod}\mathbf{x} = \mathbf{y}\]

Subframe number

Starting symbol

Number of PRACH slots within a subframe

\(N_{t}^{\mathrm{RA,slot}}\),number of time-domain PRACH occasions within a PRACH slot<br>

\(N^{\mathrm{RA}}_{\mathrm{dur}}\),PRACH duration<br>

\(x\)

\(y\)

0

0

16

1

9

0

-

-

0

1

0

8

1

9

0

-

-

0

2

0

4

1

9

0

-

-

0

3

0

2

0

9

0

-

-

0

4

0

2

1

9

0

-

-

0

5

0

2

0

4

0

-

-

0

6

0

2

1

4

0

-

-

0

7

0

1

0

9

0

-

-

0

8

0

1

0

8

0

-

-

0

9

0

1

0

7

0

-

-

0

10

0

1

0

6

0

-

-

0

11

0

1

0

5

0

-

-

0

12

0

1

0

4

0

-

-

0

13

0

1

0

3

0

-

-

0

14

0

1

0

2

0

-

-

0

15

0

1

0

1,6

0

 

 

0

16

0

1

0

1,6

7

-

-

0

17

0

1

0

4,9

0

-

-

0

18

0

1

0

3,8

0

-

-

0

19

0

1

0

2,7

0

-

-

0

20

0

1

0

8,9

0

-

-

0

21

0

1

0

4,8,9

0

-

-

0

22

0

1

0

3,4,9

0

-

-

0

23

0

1

0

7,8,9

0

-

-

0

24

0

1

0

3,4,8,9

0

-

-

0

25

0

1

0

6,7,8,9

0

-

-

0

26

0

1

0

1,4,6,9

0

-

-

0

27

0

1

0

1,3,5,7,9

0

-

-

0

28

1

16

1

7

0

-

-

0

29

1

8

1

7

0

-

-

0

30

1

4

1

7

0

-

-

0

31

1

2

0

7

0

-

-

0

32

1

2

1

7

0

-

-

0

33

1

1

0

7

0

-

-

0

34

2

16

1

6

0

-

-

0

35

2

8

1

6

0

-

-

0

36

2

4

1

6

0

-

-

0

37

2

2

0

6

7

-

-

0

38

2

2

1

6

7

-

-

0

39

2

1

0

6

7

-

-

0

40

3

16

1

9

0

-

-

0

41

3

8

1

9

0

-

-

0

42

3

4

1

9

0

-

-

0

43

3

2

0

9

0

-

-

0

44

3

2

1

9

0

-

-

0

45

3

2

0

4

0

-

-

0

46

3

2

1

4

0

-

-

0

47

3

1

0

9

0

-

-

0

48

3

1

0

8

0

-

-

0

49

3

1

0

7

0

-

-

0

50

3

1

0

6

0

-

-

0

51

3

1

0

5

0

-

-

0

52

3

1

0

4

0

-

-

0

53

3

1

0

3

0

-

-

0

54

3

1

0

2

0

-

-

0

55

3

1

0

1,6

0

-

-

0

56

3

1

0

1,6

7

-

-

0

57

3

1

0

4,9

0

-

-

0

58

3

1

0

3,8

0

-

-

0

59

3

1

0

2,7

0

-

-

0

60

3

1

0

8,9

0

-

-

0

61

3

1

0

4,8,9

0

-

-

0

62

3

1

0

3,4,9

0

-

-

0

63

3

1

0

7,8,9

0

-

-

0

64

3

1

0

3,4,8,9

0

-

-

0

65

3

1

0

1,4,6,9

0

-

-

0

66

3

1

0

1,3,5,7,9

0

-

-

0

67

A1

16

1

9

0

2

6

2

68

A1

8

1

9

0

2

6

2

69

A1

4

1

9

0

1

6

2

70

A1

2

1

9

0

1

6

2

71

A1

2

1

4,9

7

1

3

2

72

A1

2

1

7,9

7

1

3

2

73

A1

2

1

7,9

0

1

6

2

74

A1

2

1

8,9

0

2

6

2

75

A1

2

1

4,9

0

2

6

2

76

A1

2

1

2,3,4,7,8,9

0

1

6

2

77

A1

1

0

9

0

2

6

2

78

A1

1

0

9

7

1

3

2

79

A1

1

0

9

0

1

6

2

80

A1

1

0

8,9

0

2

6

2

81

A1

1

0

4,9

0

1

6

2

82

A1

1

0

7,9

7

1

3

2

83

A1

1

0

3,4,8,9

0

1

6

2

84

A1

1

0

3,4,8,9

0

2

6

2

85

A1

1

0

1,3,5,7,9

0

1

6

2

86

A1

1

0

0,1,2,3,4,5,6,7,8,9

7

1

3

2

87

A2

16

1

9

0

2

3

4

88

A2

8

1

9

0

2

3

4

89

A2

4

1

9

0

1

3

4

90

A2

2

1

7,9

0

1

3

4

91

A2

2

1

8,9

0

2

3

4

92

A2

2

1

7,9

9

1

1

4

93

A2

2

1

4,9

9

1

1

4

94

A2

2

1

4,9

0

2

3

4

95

A2

2

1

2,3,4,7,8,9

0

1

3

4

96

A2

1

0

2

0

1

3

4

97

A2

1

0

7

0

1

3

4

98

A2

2

1

9

0

1

3

4

99

A2

1

0

9

0

2

3

4

100

A2

1

0

9

9

1

1

4

101

A2

1

0

9

0

1

3

4

102

A2

1

0

2,7

0

1

3

4

103

A2

1

0

8,9

0

2

3

4

104

A2

1

0

4,9

0

1

3

4

105

A2

1

0

7,9

9

1

1

4

106

A2

1

0

3,4,8,9

0

1

3

4

107

A2

1

0

3,4,8,9

0

2

3

4

108

A2

1

0

1,3,5,7,9

0

1

3

4

109

A2

1

0

0,1,2,3,4,5,6,7,8,9

9

1

1

4

110

A3

16

1

9

0

2

2

6

111

A3

8

1

9

0

2

2

6

112

A3

4

1

9

0

1

2

6

113

A3

2

1

4,9

7

1

1

6

114

A3

2

1

7,9

7

1

1

6

115

A3

2

1

7,9

0

1

2

6

116

A3

2

1

4,9

0

2

2

6

117

A3

2

1

8,9

0

2

2

6

118

A3

2

1

2,3,4,7,8,9

0

1

2

6

119

A3

1

0

2

0

1

2

6

120

A3

1

0

7

0

1

2

6

121

A3

2

1

9

0

1

2

6

122

A3

1

0

9

0

2

2

6

123

A3

1

0

9

7

1

1

6

124

A3

1

0

9

0

1

2

6

125

A3

1

0

2,7

0

1

2

6

126

A3

1

0

8,9

0

2

2

6

127

A3

1

0

4,9

0

1

2

6

128

A3

1

0

7,9

7

1

1

6

129

A3

1

0

3,4,8,9

0

1

2

6

130

A3

1

0

3,4,8,9

0

2

2

6

131

A3

1

0

1,3,5,7,9

0

1

2

6

132

A3

1

0

0,1,2,3,4,5,6,7,8,9

7

1

1

6

133

B1

4

1

9

2

1

6

2

134

B1

2

1

9

2

1

6

2

135

B1

2

1

7,9

2

1

6

2

136

B1

2

1

4,9

8

1

3

2

137

B1

2

1

4,9

2

2

6

2

138

B1

1

0

9

2

2

6

2

139

B1

1

0

9

8

1

3

2

140

B1

1

0

9

2

1

6

2

141

B1

1

0

8,9

2

2

6

2

142

B1

1

0

4,9

2

1

6

2

143

B1

1

0

7,9

8

1

3

2

144

B1

1

0

1,3,5,7,9

2

1

6

2

145

B4

16

1

9

0

2

1

12

146

B4

8

1

9

0

2

1

12

147

B4

4

1

9

2

1

1

12

148

B4

2

1

9

0

1

1

12

149

B4

2

1

9

2

1

1

12

150

B4

2

1

7,9

2

1

1

12

151

B4

2

1

4,9

2

1

1

12

152

B4

2

1

4,9

0

2

1

12

153

B4

2

1

8,9

0

2

1

12

154

B4

2

1

2,3,4,7,8,9

0

1

1

12

155

B4

1

0

1

0

1

1

12

156

B4

1

0

2

0

1

1

12

157

B4

1

0

4

0

1

1

12

158

B4

1

0

7

0

1

1

12

159

B4

1

0

9

0

1

1

12

160

B4

1

0

9

2

1

1

12

161

B4

1

0

9

0

2

1

12

162

B4

1

0

4,9

2

1

1

12

163

B4

1

0

7,9

2

1

1

12

164

B4

1

0

8,9

0

2

1

12

165

B4

1

0

3,4,8,9

2

1

1

12

166

B4

1

0

1,3,5,7,9

2

1

1

12

167

B4

1

0

0,1,2,3,4,5,6,7,8,9

0

2

1

12

168

B4

1

0

0,1,2,3,4,5,6,7,8,9

2

1

1

12

169

C0

16

1

9

2

2

6

2

170

C0

8

1

9

2

2

6

2

171

C0

4

1

9

2

1

6

2

172

C0

2

1

9

2

1

6

2

173

C0

2

1

8,9

2

2

6

2

174

C0

2

1

7,9

2

1

6

2

175

C0

2

1

7,9

8

1

3

2

176

C0

2

1

4,9

8

1

3

2

177

C0

2

1

4,9

2

2

6

2

178

C0

2

1

2,3,4,7,8,9

2

1

6

2

179

C0

1

0

9

2

2

6

2

180

C0

1

0

9

8

1

3

2

181

C0

1

0

9

2

1

6

2

182

C0

1

0

8,9

2

2

6

2

183

C0

1

0

4,9

2

1

6

2

184

C0

1

0

7,9

8

1

3

2

185

C0

1

0

3,4,8,9

2

1

6

2

186

C0

1

0

3,4,8,9

2

2

6

2

187

C0

1

0

1,3,5,7,9

2

1

6

2

188

C0

1

0

0,1,2,3,4,5,6,7,8,9

8

1

3

2

189

C2

16

1

9

2

2

2

6

190

C2

8

1

9

2

2

2

6

191

C2

4

1

9

2

1

2

6

192

C2

2

1

9

2

1

2

6

193

C2

2

1

8,9

2

2

2

6

194

C2

2

1

7,9

2

1

2

6

195

C2

2

1

7,9

8

1

1

6

196

C2

2

1

4,9

8

1

1

6

197

C2

2

1

4,9

2

2

2

6

198

C2

2

1

2,3,4,7,8,9

2

1

2

6

199

C2

8

1

9

8

2

1

6

200

C2

4

1

9

8

1

1

6

201

C2

1

0

9

2

2

2

6

202

C2

1

0

9

8

1

1

6

203

C2

1

0

9

2

1

2

6

204

C2

1

0

8,9

2

2

2

6

205

C2

1

0

4,9

2

1

2

6

206

C2

1

0

7,9

8

1

1

6

207

C2

1

0

3,4,8,9

2

1

2

6

208

C2

1

0

3,4,8,9

2

2

2

6

209

C2

1

0

1,3,5,7,9

2

1

2

6

210

C2

1

0

0,1,2,3,4,5,6,7,8,9

8

1

1

6

211

A1/B1

2

1

9

2

1

6

2

212

A1/B1

2

1

4,9

8

1

3

2

213

A1/B1

2

1

7,9

8

1

3

2

214

A1/B1

2

1

7,9

2

1

6

2

215

A1/B1

2

1

4,9

2

2

6

2

216

A1/B1

2

1

8,9

2

2

6

2

217

A1/B1

1

0

9

2

2

6

2

218

A1/B1

1

0

9

8

1

3

2

219

A1/B1

1

0

9

2

1

6

2

220

A1/B1

1

0

8,9

2

2

6

2

221

A1/B1

1

0

4,9

2

1

6

2

222

A1/B1

1

0

7,9

8

1

3

2

223

A1/B1

1

0

3,4,8,9

2

2

6

2

224

A1/B1

1

0

1,3,5,7,9

2

1

6

2

225

A1/B1

1

0

0,1,2,3,4,5,6,7,8,9

8

1

3

2

226

A2/B2

2

1

9

0

1

3

4

227

A2/B2

2

1

4,9

6

1

2

4

228

A2/B2

2

1

7,9

6

1

2

4

229

A2/B2

2

1

4,9

0

2

3

4

230

A2/B2

2

1

8,9

0

2

3

4

231

A2/B2

1

0

9

0

2

3

4

232

A2/B2

1

0

9

6

1

2

4

233

A2/B2

1

0

9

0

1

3

4

234

A2/B2

1

0

8,9

0

2

3

4

235

A2/B2

1

0

4,9

0

1

3

4

236

A2/B2

1

0

7,9

6

1

2

4

237

A2/B2

1

0

3,4,8,9

0

1

3

4

238

A2/B2

1

0

3,4,8,9

0

2

3

4

239

A2/B2

1

0

1,3,5,7,9

0

1

3

4

240

A2/B2

1

0

0,1,2,3,4,5,6,7,8,9

6

1

2

4

241

A3/B3

2

1

9

0

1

2

6

242

A3/B3

2

1

4,9

2

1

2

6

243

A3/B3

2

1

7,9

0

1

2

6

244

A3/B3

2

1

7,9

2

1

2

6

245

A3/B3

2

1

4,9

0

2

2

6

246

A3/B3

2

1

8,9

0

2

2

6

247

A3/B3

1

0

9

0

2

2

6

248

A3/B3

1

0

9

2

1

2

6

249

A3/B3

1

0

9

0

1

2

6

250

A3/B3

1

0

8,9

0

2

2

6

251

A3/B3

1

0

4,9

0

1

2

6

252

A3/B3

1

0

7,9

2

1

2

6

253

A3/B3

1

0

3,4,8,9

0

2

2

6

254

A3/B3

1

0

1,3,5,7,9

0

1

2

6

255

A3/B3

1

0

0,1,2,3,4,5,6,7,8,9

2

1

2

6

256

0

16

1

7

0

-

-

0

257

0

8

1

7

0

-

-

0

258

0

4

1

7

0

-

-

0

259

0

2

0

7

0

-

-

0

260

0

2

1

7

0

-

-

0

261

0

2

0

2

0

-

-

0

262

0

2

1

2

0

-

-

0

 

Table 6.3.3.2-4: Random access configurations for FR2 and unpaired spectrum, and for FR2-NTN and paired spectrum.

PRACHConfig. <br>Index<br>

Preamble format

\[\mathbf{n}_{\text{f}}\text{mod}\mathbf{x} = \mathbf{y}\]

Slot number

Starting symbol

Number of PRACH slots within a 60 kHz slot

\(N_{t}^{\mathrm{RA,slot}}\),number of time-domain PRACH occasions within a PRACH slot<br>

\(N^{\mathrm{RA}}_{\mathrm{dur}}\),PRACH duration<br>

\(x\)

\(y\)

0

A1

16

1

4,9,14,19,24,29,34,39

0

2

6

2

1

A1

16

1

3,7,11,15,19,23,27,31,35,39

0

1

6

2

2

A1

8

1,2

9,19,29,39

0

2

6

2

3

A1

8

1

4,9,14,19,24,29,34,39

0

2

6

2

4

A1

8

1

3,7,11,15,19,23,27,31,35,39

0

1

6

2

5

A1

4

1

4,9,14,19,24,29,34,39

0

1

6

2

6

A1

4

1

4,9,14,19,24,29,34,39

0

2

6

2

7

A1

4

1

3,7,11,15,19,23,27,31,35,39

0

1

6

2

8

A1

2

1

7,15,23,31,39

0

2

6

2

9

A1

2

1

4,9,14,19,24,29,34,39

0

1

6

2

10

A1

2

1

4,9,14,19,24,29,34,39

0

2

6

2

11

A1

2

1

3,7,11,15,19,23,27,31,35,39

0

1

6

2

12

A1

1

0

19,39

7

1

3

2

13

A1

1

0

3,5,7

0

1

6

2

14

A1

1

0

24,29,34,39

7

1

3

2

15

A1

1

0

9,19,29,39

7

2

3

2

16

A1

1

0

17,19,37,39

0

1

6

2

17

A1

1

0

9,19,29,39

0

2

6

2

18

A1

1

0

4,9,14,19,24,29,34,39

0

1

6

2

19

A1

1

0

4,9,14,19,24,29,34,39

7

1

3

2

20

A1

1

0

3,5,7,9,11,13

7

1

3

2

21

A1

1

0

23,27,31,35,39

7

1

3

2

22

A1

1

0

7,15,23,31,39

0

1

6

2

23

A1

1

0

23,27,31,35,39

0

1

6

2

24

A1

1

0

13,14,15, 29,30,31,37,38,39

7

2

3

2

25

A1

1

0

3,7,11,15,19,23,27,31,35,39

7

1

3

2

26

A1

1

0

3,7,11,15,19,23,27,31,35,39

0

1

6

2

27

A1

1

0

1,3,5,7,…,37,39

0

1

6

2

28

A1

1

0

0,1,2,…,39

7

1

3

2

29

A2

16

1

4,9,14,19,24,29,34,39

0

2

3

4

30

A2

16

1

3,7,11,15,19,23,27,31,35,39

0

1

3

4

31

A2

8

1

4,9,14,19,24,29,34,39

0

2

3

4

32

A2

8

1

3,7,11,15,19,23,27,31,35,39

0

1

3

4

33

A2

8

1,2

9,19,29,39

0

2

3

4

34

A2

4

1

4,9,14,19,24,29,34,39

0

1

3

4

35

A2

4

1

4,9,14,19,24,29,34,39

0

2

3

4

36

A2

4

1

3,7,11,15,19,23,27,31,35,39

0

1

3

4

37

A2

2

1

7,15,23,31,39

0

2

3

4

38

A2

2

1

4,9,14,19,24,29,34,39

0

1

3

4

39

A2

2

1

4,9,14,19,24,29,34,39

0

2

3

4

40

A2

2

1

3,7,11,15,19,23,27,31,35,39

0

1

3

4

41

A2

1

0

19,39

5

1

2

4

42

A2

1

0

3,5,7

0

1

3

4

43

A2

1

0

24,29,34,39

5

1

2

4

44

A2

1

0

9,19,29,39

5

2

2

4

45

A2

1

0

17,19,37,39

0

1

3

4

46

A2

1

0

9, 19, 29, 39

0

2

3

4

47

A2

1

0

7,15,23,31,39

0

1

3

4

48

A2

1

0

23,27,31,35,39

5

1

2

4

49

A2

1

0

23,27,31,35,39

0

1

3

4

50

A2

1

0

3,5,7,9,11,13

5

1

2

4

51

A2

1

0

3,5,7,9,11,13

0

1

3

4

52

A2

1

0

4,9,14,19,24,29,34,39

5

1

2

4

53

A2

1

0

4,9,14,19,24,29,34,39

0

1

3

4

54

A2

1

0

13,14,15, 29,30,31,37,38,39

5

2

2

4

55

A2

1

0

3,7,11,15,19,23,27,31,35,39

5

1

2

4

56

A2

1

0

3,7,11,15,19,23,27,31,35,39

0

1

3

4

57

A2

1

0

1,3,5,7,…,37,39

0

1

3

4

58

A2

1

0

0,1,2,…,39

5

1

2

4

59

A3

16

1

4,9,14,19,24,29,34,39

0

2

2

6

60

A3

16

1

3,7,11,15,19,23,27,31,35,39

0

1

2

6

61

A3

8

1

4,9,14,19,24,29,34,39

0

2

2

6

62

A3

8

1

3,7,11,15,19,23,27,31,35,39

0

1

2

6

63

A3

8

1,2

9,19,29,39

0

2

2

6

64

A3

4

1

4,9,14,19,24,29,34,39

0

1

2

6

65

A3

4

1

4,9,14,19,24,29,34,39

0

2

2

6

66

A3

4

1

3,7,11,15,19,23,27,31,35,39

0

1

2

6

67

A3

2

1

4,9,14,19,24,29,34,39

0

1

2

6

68

A3

2

1

4,9,14,19,24,29,34,39

0

2

2

6

69

A3

2

1

3,7,11,15,19,23,27,31,35,39

0

1

2

6

70

A3

1

0

19,39

7

1

1

6

71

A3

1

0

3,5,7

0

1

2

6

72

A3

1

0

9,11,13

2

1

2

6

73

A3

1

0

24,29,34,39

7

1

1

6

74

A3

1

0

9,19,29,39

7

2

1

6

75

A3

1

0

17,19,37,39

0

1

2

6

76

A3

1

0

9,19,29,39

0

2

2

6

77

A3

1

0

7,15,23,31,39

0

1

2

6

78

A3

1

0

23,27,31,35,39

7

1

1

6

79

A3

1

0

23,27,31,35,39

0

1

2

6

80

A3

1

0

3,5,7,9,11,13

0

1

2

6

81

A3

1

0

3,5,7,9,11,13

7

1

1

6

82

A3

1

0

4,9,14,19,24,29,34,39

0

1

2

6

83

A3

1

0

4,9,14,19,24,29,34,39

7

1

1

6

84

A3

1

0

13,14,15, 29,30,31,37,38,39

7

2

1

6

85

A3

1

0

3,7,11,15,19,23,27,31,35,39

7

1

1

6

86

A3

1

0

3,7,11,15,19,23,27,31,35,39

0

1

2

6

87

A3

1

0

1,3,5,7,…,37,39

0

1

2

6

88

A3

1

0

0,1,2,…,39

7

1

1

6

89

B1

16

1

4,9,14,19,24,29,34,39

2

2

6

2

90

B1

8

1

4,9,14,19,24,29,34,39

2

2

6

2

91

B1

8

1,2

9,19,29,39

2

2

6

2

92

B1

4

1

4,9,14,19,24,29,34,39

2

2

6

2

93

B1

2

1

4,9,14,19,24,29,34,39

2

2

6

2

94

B1

2

1

3,7,11,15,19,23,27,31,35,39

2

1

6

2

95

B1

1

0

19,39

8

1

3

2

96

B1

1

0

3,5,7

2

1

6

2

97

B1

1

0

24,29,34,39

8

1

3

2

98

B1

1

0

9,19,29,39

8

2

3

2

99

B1

1

0

17,19,37,39

2

1

6

2

100

B1

1

0

9,19,29,39

2

2

6

2

101

B1

1

0

7,15,23,31,39

2

1

6

2

102

B1

1

0

23,27,31,35,39

8

1

3

2

103

B1

1

0

23,27,31,35,39

2

1

6

2

104

B1

1

0

3,5,7,9,11,13

8

1

3

2

105

B1

1

0

4,9,14,19,24,29,34,39

8

1

3

2

106

B1

1

0

4,9,14,19,24,29,34,39

2

1

6

2

107

B1

1

0

3,7,11,15,19,23,27,31,35,39

8

1

3

2

108

B1

1

0

13,14,15, 29,30,31,37,38,39

8

2

3

2

109

B1

1

0

3,7,11,15,19,23,27,31,35,39

2

1

6

2

110

B1

1

0

1,3,5,7,…,37,39

2

1

6

2

111

B1

1

0

0,1,2,…,39

8

1

3

2

112

B4

16

1,2

4,9,14,19,24,29,34,39

0

2

1

12

113

B4

16

1,2

3,7,11,15,19,23,27,31,35,39

0

1

1

12

114

B4

8

1,2

4,9,14,19,24,29,34,39

0

2

1

12

115

B4

8

1,2

3,7,11,15,19,23,27,31,35,39

0

1

1

12

116

B4

8

1,2

9,19,29,39

0

2

1

12

117

B4

4

1

4,9,14,19,24,29,34,39

0

1

1

12

118

B4

4

1

4,9,14,19,24,29,34,39

0

2

1

12

119

B4

4

1,2

3,7,11,15,19,23,27,31,35,39

0

1

1

12

120

B4

2

1

7,15,23,31,39

2

2

1

12

121

B4

2

1

4,9,14,19,24,29,34,39

0

1

1

12

122

B4

2

1

4,9,14,19,24,29,34,39

0

2

1

12

123

B4

2

1

3,7,11,15,19,23,27,31,35,39

0

1

1

12

124

B4

1

0

19, 39

2

2

1

12

125

B4

1

0

17, 19, 37, 39

0

1

1

12

126

B4

1

0

24,29,34,39

2

1

1

12

127

B4

1

0

9,19,29,39

2

2

1

12

128

B4

1

0

9,19,29,39

0

2

1

12

129

B4

1

0

7,15,23,31,39

0

1

1

12

130

B4

1

0

7,15,23,31,39

0

2

1

12

131

B4

1

0

23,27,31,35,39

0

1

1

12

132

B4

1

0

23,27,31,35,39

2

2

1

12

133

B4

1

0

9,11,13,15,17,19

0

1

1

12

134

B4

1

0

3,5,7,9,11,13

2

1

1

12

135

B4

1

0

4,9,14,19,24,29,34,39

0

1

1

12

136

B4

1

0

4,9,14,19,24,29,34,39

2

2

1

12

137

B4

1

0

13,14,15, 29,30,31,37,38,39

2

2

1

12

138

B4

1

0

3,7,11,15,19,23,27,31,35,39

0

1

1

12

139

B4

1

0

3,7,11,15,19,23,27,31,35,39

2

1

1

12

140

B4

1

0

3, 5, 7, …, 23,25

2

1

1

12

141

B4

1

0

3, 5, 7, …, 23,25

0

2

1

12

142

B4

1

0

1,3,5,7,…,37,39

0

1

1

12

143

B4

1

0

0, 1, 2,…, 39

2

1

1

12

144

C0

16

1

4,9,14,19,24,29,34,39

0

2

7

2

145

C0

16

1

3,7,11,15,19,23,27,31,35,39

0

1

7

2

146

C0

8

1

4,9,14,19,24,29,34,39

0

1

7

2

147

C0

8

1

3,7,11,15,19,23,27,31,35,39

0

1

7

2

148

C0

8

1,2

9,19,29,39

0

2

7

2

149

C0

4

1

4,9,14,19,24,29,34,39

0

1

7

2

150

C0

4

1

4,9,14,19,24,29,34,39

0

2

7

2

151

C0

4

1

3,7,11,15,19,23,27,31,35,39

0

1

7

2

152

C0

2

1

7,15,23,31,39

0

2

7

2

153

C0

2

1

4,9,14,19,24,29,34,39

0

1

7

2

154

C0

2

1

4,9,14,19,24,29,34,39

0

2

7

2

155

C0

2

1

3,7,11,15,19,23,27,31,35,39

0

1

7

2

156

C0

1

0

19,39

8

1

3

2

157

C0

1

0

3,5,7

0

1

7

2

158

C0

1

0

24,29,34,39

8

1

3

2

159

C0

1

0

9,19,29,39

8

2

3

2

160

C0

1

0

17,19,37,39

0

1

7

2

161

C0

1

0

9,19,29,39

0

2

7

2

162

C0

1

0

23,27,31,35,39

8

1

3

2

163

C0

1

0

7,15,23,31,39

0

1

7

2

164

C0

1

0

23,27,31,35,39

0

1

7

2

165

C0

1

0

3,5,7,9,11,13

8

1

3

2

166

C0

1

0

4,9,14,19,24,29,34,39

8

1

3

2

167

C0

1

0

4,9,14,19,24,29,34,39

0

1

7

2

168

C0

1

0

13,14,15, 29,30,31,37,38,39

8

2

3

2

169

C0

1

0

3,7,11,15,19,23,27,31,35,39

8

1

3

2

170

C0

1

0

3,7,11,15,19,23,27,31,35,39

0

1

7

2

171

C0

1

0

1,3,5,7,…,37,39

0

1

7

2

172

C0

1

0

0,1,2,…,39

8

1

3

2

173

C2

16

1

4,9,14,19,24,29,34,39

0

2

2

6

174

C2

16

1

3,7,11,15,19,23,27,31,35,39

0

1

2

6

175

C2

8

1

4,9,14,19,24,29,34,39

0

2

2

6

176

C2

8

1

3,7,11,15,19,23,27,31,35,39

0

1

2

6

177

C2

8

1,2

9,19,29,39

0

2

2

6

178

C2

4

1

4,9,14,19,24,29,34,39

0

1

2

6

179

C2

4

1

4,9,14,19,24,29,34,39

0

2

2

6

180

C2

4

1

3,7,11,15,19,23,27,31,35,39

0

1

2

6

181

C2

2

1

7,15,23,31,39

2

2

2

6

182

C2

2

1

4,9,14,19,24,29,34,39

0

1

2

6

183

C2

2

1

4,9,14,19,24,29,34,39

0

2

2

6

184

C2

2

1

3,7,11,15,19,23,27,31,35,39

0

1

2

6

185

C2

1

0

19,39

2

1

2

6

186

C2

1

0

3,5,7

0

1

2

6

187

C2

1

0

24,29,34,39

7

1

1

6

188

C2

1

0

9,19,29,39

7

2

1

6

189

C2

1

0

17,19,37,39

0

1

2

6

190

C2

1

0

9,19,29,39

2

2

2

6

191

C2

1

0

7,15,23,31,39

2

1

2

6

192

C2

1

0

3,5,7,9,11,13

7

1

1

6

193

C2

1

0

23,27,31,35,39

7

2

1

6

194

C2

1

0

23,27,31,35,39

0

1

2

6

195

C2

1

0

4,9,14,19,24,29,34,39

7

2

1

6

196

C2

1

0

4,9,14,19,24,29,34,39

2

1

2

6

197

C2

1

0

13,14,15, 29,30,31,37,38,39

7

2

1

6

198

C2

1

0

3,7,11,15,19,23,27,31,35,39

7

1

1

6

199

C2

1

0

3,7,11,15,19,23,27,31,35,39

0

1

2

6

200

C2

1

0

1,3,5,7,…,37,39

0

1

2

6

201

C2

1

0

0,1,2,…,39

7

1

1

6

202

A1/B1

16

1

4,9,14,19,24,29,34,39

2

1

6

2

203

A1/B1

16

1

3,7,11,15,19,23,27,31,35,39

2

1

6

2

204

A1/B1

8

1

4,9,14,19,24,29,34,39

2

1

6

2

205

A1/B1

8

1

3,7,11,15,19,23,27,31,35,39

2

1

6

2

206

A1/B1

4

1

4,9,14,19,24,29,34,39

2

1

6

2

207

A1/B1

4

1

3,7,11,15,19,23,27,31,35,39

2

1

6

2

208

A1/B1

2

1

4,9,14,19,24,29,34,39

2

1

6

2

209

A1/B1

1

0

19,39

8

1

3

2

210

A1/B1

1

0

9,19,29,39

8

1

3

2

211

A1/B1

1

0

17,19,37,39

2

1

6

2

212

A1/B1

1

0

9,19,29,39

2

2

6

2

213

A1/B1

1

0

23,27,31,35,39

8

1

3

2

214

A1/B1

1

0

7,15,23,31,39

2

1

6

2

215

A1/B1

1

0

23,27,31,35,39

2

1

6

2

216

A1/B1

1

0

4,9,14,19,24,29,34,39

8

1

3

2

217

A1/B1

1

0

4,9,14,19,24,29,34,39

2

1

6

2

218

A1/B1

1

0

3,7,11,15,19,23,27,31,35,39

2

1

6

2

219

A1/B1

1

0

1,3,5,7,…,37,39

2

1

6

2

220

A2/B2

16

1

4,9,14,19,24,29,34,39

2

1

3

4

221

A2/B2

16

1

3,7,11,15,19,23,27,31,35,39

2

1

3

4

222

A2/B2

8

1

4,9,14,19,24,29,34,39

2

1

3

4

223

A2/B2

8

1

3,7,11,15,19,23,27,31,35,39

2

1

3

4

224

A2/B2

4

1

4,9,14,19,24,29,34,39

2

1

3

4

225

A2/B2

4

1

3,7,11,15,19,23,27,31,35,39

2

1

3

4

226

A2/B2

2

1

4,9,14,19,24,29,34,39

2

1

3

4

227

A2/B2

1

0

19,39

6

1

2

4

228

A2/B2

1

0

9,19,29,39

6

1

2

4

229

A2/B2

1

0

17,19,37,39

2

1

3

4

230

A2/B2

1

0

9,19,29,39

2

2

3

4

231

A2/B2

1

0

23,27,31,35,39

6

1

2

4

232

A2/B2

1

0

7,15,23,31,39

2

1

3

4

233

A2/B2

1

0

23,27,31,35,39

2

1

3

4

234

A2/B2

1

0

4,9,14,19,24,29,34,39

6

1

2

4

235

A2/B2

1

0

4,9,14,19,24,29,34,39

2

1

3

4

236

A2/B2

1

0

3,7,11,15,19,23,27,31,35,39

2

1

3

4

237

A2/B2

1

0

1,3,5,7,…,37,39

2

1

3

4

238

A3/B3

16

1

4,9,14,19,24,29,34,39

2

1

2

6

239

A3/B3

16

1

3,7,11,15,19,23,27,31,35,39

2

1

2

6

240

A3/B3

8

1

4,9,14,19,24,29,34,39

2

1

2

6

241

A3/B3

8

1

3,7,11,15,19,23,27,31,35,39

2

1

2

6

242

A3/B3

4

1

4,9,14,19,24,29,34,39

2

1

2

6

243

A3/B3

4

1

3,7,11,15,19,23,27,31,35,39

2

1

2

6

244

A3/B3

2

1

4,9,14,19,24,29,34,39

2

1

2

6

245

A3/B3

1

0

19,39

2

1

2

6

246

A3/B3

1

0

9,19,29,39

2

1

2

6

247

A3/B3

1

0

17,19,37,39

2

1

2

6

248

A3/B3

1

0

9,19,29,39

2

2

2

6

249

A3/B3

1

0

7,15,23,31,39

2

1

2

6

250

A3/B3

1

0

23,27,31,35,39

2

1

2

6

251

A3/B3

1

0

23,27,31,35,39

2

2

2

6

252

A3/B3

1

0

4,9,14,19,24,29,34,39

2

1

2

6

253

A3/B3

1

0

4,9,14,19,24,29,34,39

2

2

2

6

254

A3/B3

1

0

3,7,11,15,19,23,27,31,35,39

2

1

2

6

255

A3/B3

1

0

1,3,5,7,…,37,39

2

1

2

6

 

6 .4    Physical signals #

6 .4.1    Reference signals #

6 .4.1.1    Demodulation reference signal for PUSCH #

6.4.1. 1.1    Sequence generation #
6.4.1.1.1.1    Sequence generation when transform precoding is disabled="disabled" #

If transform precoding for PUSCH is not enabled, the sequence \(r(n)\) shall be generated according to

\(r(n)=\frac{1}{\sqrt{2}}\left(1-2\cdot c(2n)\right)+j\frac{1}{\sqrt{2}}\left(1-2\cdot c(2n+1)\right)\).

where the pseudo-random sequence \(c(i)\) is defined in clause 5.2.1. The pseudo-random sequence generator shall be initialized with

\[c_{\text{init}} = \left( {2^{17}\left( {N_{\text{symb}}^{\text{slot}}n_{\text{s,f}}^{\mu} + l + 1} \right)\left( {2N_{\text{ID}}^{{\bar{n}}_{\text{SCID}}^{\bar{\lambda}}} + 1} \right) + 2^{17}\left\lfloor \frac{\bar{\lambda}}{2} \right\rfloor + 2N_{\text{ID}}^{{\bar{n}}_{\text{SCID}}^{\bar{\lambda}}} + {\bar{n}}_{\text{SCID}}^{\bar{\lambda}}} \right)\text{mod}2^{31}\]

where \(l\) is the OFDM symbol number within the slot, \(n_{\text{s,f}}^{\mu}\) is the slot number within a frame, and

-    \(N_{\text{ID}}^{0},N_{\text{ID}}^{1} \in \left\{ {0,1,\ldots,65535} \right\}\) are given by the higher-layer parameters scramblingID0 and scramblingID1, respectively, in the DMRS-UplinkConfig IE if provided and the PUSCH is scheduled by DCI format 0_1, 0_2, or 0_3, or by a PUSCH transmission with a configured grant;

-    \(N_{\text{ID}}^{0} \in \left\{ {0,1,\ldots,65535} \right\}\) is given by the higher-layer parameter scramblingID0 in the DMRS-UplinkConfig IE if provided and the PUSCH is scheduled by DCI format 0_0 with the CRC scrambled by C-RNTI, MCS-C-RNTI, or CS-RNTI;

-    \(N_{\text{ID}}^{0},N_{\text{ID}}^{1} \in \left\{ {0,1,\ldots,65535} \right\}\) are, for each msgA PUSCH configuration, given by the higher-layer parameters msgA-ScramblingID0 and msgA-ScramblingID1, respectively, in the msgA-DMRS-Config IE if provided and the PUSCH transmission is triggered by a Type-2 random access procedure as described in clause 8.1A of [5, TS 38.213];

-    \(N_{\text{ID}}^{{\bar{n}}_{\text{SCID}}^{\bar{\lambda}}} = N_{\text{ID}}^{\text{cell}}\) otherwise;

-    \({\bar{n}}_{\text{SCID}}^{\bar{\lambda}}\) and \(\bar{\lambda}\) are given by

-    if the higher-layer parameter dmrs-Uplink in the DMRS-UplinkConfig IE is provided

nSCIDλ=nSCIDλ=0 or λ=21-nSCIDλ=1λ=λ

    where \(\lambda\) is the CDM group defined in clause 6.4.1.1.3.

-    otherwise

\[\begin{matrix} {{\bar{n}}_{\text{SCID}}^{\bar{\lambda}} = n_{\text{SCID}}} \\ {\bar{\lambda} = 0} \end{matrix}\]

The quantity \(n_{\text{SCID}} \in \left\{ 0,1 \right\}\) is

-    indicated by the DM-RS initialization field, if present, either in the DCI associated with the PUSCH transmission if DCI format 0_1, 0_2, or 0_3, in [4, TS 38.212] is used;

-    indicated by the higher layer parameter dmrs-SeqInitialization, if present, for a Type 1 PUSCH transmission with a configured grant;

-    determined by the mapping between preamble(s) and a PUSCH occasion and the associated DMRS resource for a PUSCH transmission of Type-2 random access process in [5, TS 38.213];

-    determined by the mapping between SS/PBCH block(s) and a PUSCH occasion and the associated DMRS resource for a configured-grant based PUSCH transmission in RRC_INACTIVE state [5, TS 38.213];

-    otherwise \(n_{\text{SCID}} = 0\).

6.4.1.1.1.2    Sequence generation when transform precoding is enabled #

If transform precoding for PUSCH is enabled, the reference-signal sequence \(r(n)\) shall be generated according to

\(\begin{aligned} r(n) &= r_{u,v}^{(\alpha,\delta)}(n)\\ n &= 0,1,\ldots,\frac{M_{sc}^{\mathrm{PUSCH}}}{2^{\delta}} - 1 \end{aligned}\)

where \(r_{u,v}^{({\alpha,\delta})}(n)\) with \(\delta = 1\) depends on the configuration:

-    if the higher-layer parameter dmrs-UplinkTransformPrecoding is configured, π/2-BPSK modulation is used for PUSCH, and the PUSCH transmission is not a msg3 transmission, and the transmission is not scheduled using DCI format 0_0 in a common search space, \(r_{u,v}^{({\alpha,\delta})}(n)\) is given by clause 5.2.3 with \(c_{\text{init}}\) given by

\[c_{\text{init}} = \left( {2^{17}\left( {N_{\text{symb}}^{\text{slot}}n_{\text{s,f}}^{\mu} + l + 1} \right)\left( {2N_{\text{ID}}^{n_{\text{SCID}}} + 1} \right) + 2N_{\text{ID}}^{n_{\text{SCID}}} + n_{\text{SCID}}} \right)\text{mod}2^{31}\]

    where \(n_{\text{SCID}} = 0\) unless given by the DCI according to clause 7.3.1.1.2 in [4, TS38.212] for a transmission scheduled by DCI format 0_1, or given by the DCI according to clause 7.3.1.1.3 in [4, TS38.212] for a transmission scheduled by DCI format 0_2 if the antenna ports field in the DCI format 0_2 is not 0 bit, or given by the DCI according to clause 7.3.1.1.4 in [4, TS38.212] for a transmission scheduled by DCI format 0_3, or given by the higher-layer parameter antennaPort for a PUSCH transmission scheduled by a type-1 configured grant; and

-    \(N_{\text{ID}}^{0},N_{\text{ID}}^{1} \in \left\{ {0,1,\ldots,65535} \right\}\) are given by the higher-layer parameters pi2BPSK-ScramblingID0 and pi2BPSK-ScramblingID1, respectively, in the DMRS-UplinkConfig IE if provided and the PUSCH is scheduled by DCI format 0_1, or by DCI format 0_2 if the antenna ports field in the DCI format 0_2 is not 0 bit, or by DCI format 0_3, or by a PUSCH transmission with a configured grant;

-    \(N_{\text{ID}}^{0} \in \left\{ {0,1,\ldots,65535} \right\}\) is given by the higher-layer parameter pi2BPSK-ScramblingID0 in the DMRS-UplinkConfig IE if provided and the PUSCH is scheduled by DCI format 0_0 with the CRC scrambled by C-RNTI, MCS-C-RNTI, or CS-RNTI, or by DCI format 0_2 if the antenna ports field in the DCI format 0_2 is 0 bit;

-    \(N_{\text{ID}}^{n_{\text{SCID}}} = N_{\text{ID}}^{\text{cell}}\) otherwise;

-    otherwise, \(r_{u,v}^{({\alpha,\delta})}(n)\) is given by clause 5.2.2 with \(\alpha = 0\).

The sequence group \(u = \left( {f_{\text{gh}} + n_{\text{ID}}^{\text{RS}}} \right)\text{mod}30\), where \(n_{\text{ID}}^{\text{RS}}\) is given by

-    \(n_{\text{ID}}^{\text{RS}} = n_{\text{ID}}^{\text{PUSCH}}\) if \(n_{\text{ID}}^{\text{PUSCH}}\) is configured by the higher-layer parameter nPUSCH-Identity in the DMRS-UplinkConfig IE, and

-    the higher-layer parameter dmrs-UplinkTransformPrecoding is not configured or the higher-layer parameter dmrs-UplinkTransformPrecoding is configured and π/2-BPSK modulation is not used for PUSCH, and

-    the PUSCH is neither scheduled by RAR UL grant nor scheduled by DCI format 0_0 with CRC scrambled by TC-RNTI according to clause 8.3 in [5, TS 38.213];

-    \(n_{\text{ID}}^{\text{RS}} = N_{\text{ID}}^{n_{\text{SCID}}}\) if the higher-layer parameter dmrs-UplinkTransformPrecoding is configured, π/2-BPSK modulation is used for PUSCH, the PUSCH transmission is not a msg3 transmission, and the transmission is not scheduled using DCI format 0_0 in a common search space;

-    \(n_{\text{ID}}^{\text{RS}} = N_{\text{ID}}^{\text{cell}}\) otherwise

where \(f_{gh}\) and the sequence number \(v\) are given by:

-    if neither group, nor sequence hopping is enabled

    \(\begin{aligned} f_{gh}=0\\ v=0 \end{aligned}\)

-    if group hopping is enabled and sequence hopping is disabled="disabled"

    \(f_{gh}=\left(\sum_{m=0}^{7}2^{m}c\!\left(8\left(N_{\text{symb}}^{\text{slot}}\,n_{s,f}^{\mu}+l\right)+m\right)\right)\bmod 30 v=0\)

    where the pseudo-random sequence \(c(i)\) is defined by clause 5.2.1 and shall be initialized with \(c_{init} = \left\lfloor \frac{n_{ID}^{\mathrm{RS}}}{30} \right\rfloor\) at the beginning of each radio frame

-    if sequence hopping is enabled and group hopping is disabled

    \(f_{gh}=0 v=\begin{cases} c\left(N_{symb}^{\mathrm{slot}}\,n_{s,f}^{\mu}+l\right) & \text{if } M_{ZC}\ge 6\,N_{sc}^{\mathrm{RB}}\\ 0 & \text{otherwise} \end{cases}\)

    where the pseudo-random sequence \(c(i)\) is defined by clause 5.2.1 and shall be initialized with \(c_{\mathrm{init}} = n^{\mathrm{RS}}_{\mathrm{ID}}\) at the beginning of each radio frame.

The hopping mode is controlled by higher-layer parameters:

-    for PUSCH transmission scheduled by RAR UL grant or by DCI format 0_0 with CRC scrambled by TC-RNTI, sequence hopping is disabled="disabled" and group hopping is enabled or disabled="disabled" by the higher-layer parameter groupHoppingEnabledTransformPrecoding;

-    for all other transmissions, sequence hopping and group hopping are enabled or disabled="disabled" by the respective higher-layer parameters sequenceHopping and sequenceGroupHopping if these parameters are provided, otherwise, the same hopping mode as for Msg3 shall be used.

The UE is not expected to handle the case of combined sequence hopping and group hopping.

The quantity \(l\) above is the OFDM symbol number in the slot except for the case of double-symbol DMRS in which case \(l\) is the OFDM symbol number in the slot of the first symbol of the double-symbol DMRS.

6.4.1.1.2     (void) #
6.4.1. 1.3    Precoding and mapping to physical resources #

The sequence \(r(m)\) shall be mapped to the intermediate quantity \({\overset{\sim}{a}}_{k,l}^{({\overset{\sim}{p}}_{j},\mu)}\) according to

-    if transform precoding is not enabled,

-    if the higher-layer parameter dmrs-TypeEnh is configured

a~k,lp~j,μ=wfk'wtl'r4n+k'k=8n+2k'+Δconfiguration type 112n+k'+Δconfiguration type 2, k'=0,112n+k'+Δ+4configuration type 2, k'=2,3k'=0,1,2,3l=l+l'n=0,1,j=0,1,,υ-1

-    otherwise

a~k,lp~j,μ=wfk'wtl'r2n+k'k=4n+2k'+Δconfiguration type 16n+k'+Δconfiguration type 2k'=0,1l=l+l'n=0,1,j=0,1,,υ-1

-    if transform precoding is enabled

\[\begin{matrix} {{\overset{\sim}{a}}_{k,l}^{({{\overset{\sim}{p}}_{0},\mu})} = w_{\text{f}}\left( k^{'} \right)w_{\text{t}}\left( l^{'} \right)r\left( {2n + k^{'}} \right)} \\ {k = 4n + 2k^{'} + \Delta} \\ {k^{'} = 0,1} \\ {l = \bar{l} + l'} \\ {n = 0,1,\ldots} \end{matrix}\]

where \(w_{\text{f}}\left( {k'} \right)\), \(w_{\text{t}}\left( {l'} \right)\), and \(\Delta\) are given by Tables 6.4.1.1.3-1 and 6.4.1.1.3-2 and the configuration type is given by the higher-layer parameter DMRS-UplinkConfig, and both \(k'\) and \(\Delta\) correspond to \({\overset{\sim}{p}}_{0},\ldots,{\overset{\sim}{p}}_{\nu - 1}\). The intermediate quantity \({\overset{\sim}{a}}_{k,l}^{{(\overset{\sim}{p}}_{j},\mu)} = 0\) if Δ corresponds to any other antenna ports than\({\overset{\sim}{p}}_{j}\).

The intermediate quantity \({\overset{\sim}{a}}_{k,l}^{({\overset{\sim}{p}}_{j},\mu)}\) shall be precoded, multiplied with the amplitude scaling factor \(\beta_{\text{PUSCH}}^{\text{DMRS}}\) in order to conform to the transmit power specified in [6, TS 38.214], and mapped to physical resources according to

    \(\begin{bmatrix} a_{k,l}^{({p_{0},\mu})} \\ \vdots \\ a_{k,l}^{({p_{\rho - 1},\mu})} \end{bmatrix} = \beta_{\text{PUSCH}}^{\text{DMRS}}W\begin{bmatrix} {\overset{\sim}{a}}_{k,l}^{({{\overset{\sim}{p}}_{0},\mu})} \\ \vdots \\ {\overset{\sim}{a}}_{k,l}^{({{\overset{\sim}{p}}_{\upsilon - 1},\mu})} \end{bmatrix}\)

where

-    the precoding matrix \(W\) is given by clause 6.3.1.5,

-    the set of antenna ports \(\left\{ {p_{0},\ldots,p_{\rho - 1}} \right\}\) is given by clause 6.3.1.5, and

-    the set of antenna ports \(\left\{ {{\overset{\sim}{p}}_{0},\ldots,{\overset{\sim}{p}}_{\rho - 1}} \right\}\) is given by [6, TS 38.214];

and the following conditions are fulfilled:

-    the resource elements \({\overset{\sim}{a}}_{k,l}^{({\overset{\sim}{p}}_{j},\mu)}\) are within the common resource blocks allocated for PUSCH transmission.

The reference point for \(k\) is

-    subcarrier 0 in common resource block 0 if transform precoding is not enabled, and

-    subcarrier 0 of the lowest-numbered resource block of the scheduled PUSCH allocation if transform precoding is enabled.

The reference point for \(l\) and the position \(\ell_0\) of the first DM-RS symbol depends on the mapping type:

-    for PUSCH mapping type A:

-    \(l\) is defined relative to the start of the slot if frequency hopping is disabled="disabled" and relative to the start of each hop in case frequency hopping is enabled

-    \(\ell_0\) is given by the higher-layer parameter dmrs-TypeA-Position

-    for PUSCH mapping type B:

-    \(l\) is defined relative to the start of the scheduled PUSCH resources if frequency hopping is disabled="disabled" and relative to the start of each hop in case frequency hopping is enabled

-    \(l_{0} = 0\)

The position(s) of the DM-RS symbols is given by \(\overline{l}\) and duration \(l_{\text{d}}\) where

-    \(l_{\text{d}}\) is the duration between the first OFDM symbol of the slot and the last OFDM symbol of the scheduled PUSCH resources in the slot for PUSCH mapping type A according to Tables 6.4.1.1.3-3 and 6.4.1.1.3-4 if intra-slot frequency hopping is not used, or

-    \(l_{\text{d}}\) is the duration of scheduled PUSCH resources for PUSCH mapping type B according to Tables 6.4.1.1.3-3 and 6.4.1.1.3-4 if intra-slot frequency hopping is not used, or

-    \(l_{\text{d}}\) is the duration per hop according to Table 6.4.1.1.3-6 if intra-slot frequency hopping is used.

-    if the higher-layer parameter maxLength in DMRS-UplinkConfig is not configured, or for a msgA transmission msgA-MaxLength in msgA-DMRS-Config is not configured, the tables shall be used according to single-symbol DM-RS

-    if the higher-layer parameter maxLength in DMRS-UplinkConfig is equal to 'len2', the associated DCI or configured grant configuration determines whether single-symbol or double-symbol DM-RS shall be used

-    if the higher-layer parameter msgA-MaxLength in msgA-DMRS-Config is equal to 'len2', double-symbol DM-RS shall be used

-    if the higher-layer parameter dmrs-AdditionalPosition is not set to 'pos0' and intra-slot frequency hopping is enabled according to clause 7.3.1.1.2 in [4, TS 38.212] and by higher layer, Tables 6.4.1.1.3-6 shall be used assuming dmrs-AdditionalPosition is equal to 'pos1' for each hop.

For PUSCH mapping type A,

-    the case dmrs-AdditionalPosition is equal to 'pos3' is only supported when dmrs-TypeA-Position is equal to 'pos2';

-    \(l_{\text{d}} = 4\) symbols in Table 6.4.1.1.3-4 is only applicable when dmrs-TypeA-Position is equal to 'pos2'.

For msgA transmitted using PUSCH mapping type A,

-    the case msgA-DMRS-AdditionalPosition is equal to 'pos3' is only supported when dmrs-TypeA-Position is equal to 'pos2';

-    'dmrs-AdditionalPosition' in Tables 6.4.1.1.3-3 to 6.4.1.1.3-6 shall be replaced by msgA-DMRS-AdditionalPosition;

-    only PUSCH DM-RS configuration type 1 is supported;

-    only basic DM-RS multiplexing in Table 6.4.1.1.3-5 is supported.

For msgA transmitted using PUSCH mapping type B,

-    'dmrs-AdditionalPosition' in Tables 6.4.1.1.3-3 to 6.4.1.1.3-6 shall be replaced by msgA-DMRS-AdditionalPosition;

-    only PUSCH DM-RS configuration type 1 is supported;

-    only basic DM-RS multiplexing in Table 6.4.1.1.3-5 is supported.

The time-domain index \(l'\), and the supported antenna ports \({\overset{\sim}{p}}_{j}\) are given by Table 6.4.1.1.3-5.

 

Table 6.4.1.1.3-1: Parameters for PUSCH DM-RS configuration type 1.

\[\overset{\sim}{\mathbf{p}}\]

CDM group \(\mathbf{\lambda}\)

\[\mathbf{\Delta}\]

\[\begin{bmatrix} {\mathbf{w}_{\text{f}}(0)} & \ldots & {\mathbf{w}_{\text{f}}(3)} \end{bmatrix}\]

\[\begin{bmatrix} {\mathbf{w}_{\text{t}}(0)} & {\mathbf{w}_{\text{t}}(1)} \end{bmatrix}\]

0

0

0

\[\begin{bmatrix} {+ 1} & {+ 1} & {+ 1} & {+ 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

1

0

0

\[\begin{bmatrix} {+ 1} & {- 1} & {+ 1} & {- 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

2

1

1

\[\begin{bmatrix} {+ 1} & {+ 1} & {+ 1} & {+ 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

3

1

1

\[\begin{bmatrix} {+ 1} & {- 1} & {+ 1} & {- 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

4

0

0

\[\begin{bmatrix} {+ 1} & {+ 1} & {+ 1} & {+ 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

5

0

0

\[\begin{bmatrix} {+ 1} & {- 1} & {+ 1} & {- 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

6

1

1

\[\begin{bmatrix} {+ 1} & {+ 1} & {+ 1} & {+ 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

7

1

1

\[\begin{bmatrix} {+ 1} & {- 1} & {+ 1} & {- 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

8

0

0

\[\begin{bmatrix} {+ 1} & {+ j} & {- 1} & {- j} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

9

0

0

\[\begin{bmatrix} {+ 1} & {- j} & {- 1} & {+ j} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

10

1

1

\[\begin{bmatrix} {+ 1} & {+ j} & {- 1} & {- j} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

11

1

1

\[\begin{bmatrix} {+ 1} & {- j} & {- 1} & {+ j} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

12

0

0

\[\begin{bmatrix} {+ 1} & {+ j} & {- 1} & {- j} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

13

0

0

\[\begin{bmatrix} {+ 1} & {- j} & {- 1} & {+ j} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

14

1

1

\[\begin{bmatrix} {+ 1} & {+ j} & {- 1} & {- j} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

15

1

1

\[\begin{bmatrix} {+ 1} & {- j} & {- 1} & {+ j} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

 

Table 6.4.1.1.3-2: Parameters for PUSCH DM-RS configuration type 2.

\[\overset{\sim}{\mathbf{p}}\]

CDM group \(\mathbf{\lambda}\)

\[\mathbf{\Delta}\]

\[\begin{bmatrix} {\mathbf{w}_{\text{f}}(0)} & \ldots & {\mathbf{w}_{\text{f}}(3)} \end{bmatrix}\]

\[\begin{bmatrix} {\mathbf{w}_{\text{t}}(0)} & {\mathbf{w}_{\text{t}}(1)} \end{bmatrix}\]

0

0

0

\[\begin{bmatrix} {+ 1} & {+ 1} & {+ 1} & {+ 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

1

0

0

\[\begin{bmatrix} {+ 1} & {- 1} & {+ 1} & {- 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

2

1

2

\[\begin{bmatrix} {+ 1} & {+ 1} & {+ 1} & {+ 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

3

1

2

\[\begin{bmatrix} {+ 1} & {- 1} & {+ 1} & {- 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

4

2

4

\[\begin{bmatrix} {+ 1} & {+ 1} & {+ 1} & {+ 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

5

2

4

\[\begin{bmatrix} {+ 1} & {- 1} & {+ 1} & {- 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

6

0

0

\[\begin{bmatrix} {+ 1} & {+ 1} & {+ 1} & {+ 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

7

0

0

\[\begin{bmatrix} {+ 1} & {- 1} & {+ 1} & {- 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

8

1

2

\[\begin{bmatrix} {+ 1} & {+ 1} & {+ 1} & {+ 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

9

1

2

\[\begin{bmatrix} {+ 1} & {- 1} & {+ 1} & {- 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

10

2

4

\[\begin{bmatrix} {+ 1} & {+ 1} & {+ 1} & {+ 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

11

2

4

\[\begin{bmatrix} {+ 1} & {- 1} & {+ 1} & {- 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

12

0

0

\[\begin{bmatrix} {+ 1} & {+ j} & {- 1} & {- j} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

13

0

0

\[\begin{bmatrix} {+ 1} & {- j} & {- 1} & {+ j} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

14

1

2

\[\begin{bmatrix} {+ 1} & {+ j} & {- 1} & {- j} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

15

1

2

\[\begin{bmatrix} {+ 1} & {- j} & {- 1} & {+ j} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

16

2

4

\[\begin{bmatrix} {+ 1} & {+ j} & {- 1} & {- j} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

17

2

4

\[\begin{bmatrix} {+ 1} & {- j} & {- 1} & {+ j} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

18

0

0

\[\begin{bmatrix} {+ 1} & {+ j} & {- 1} & {- j} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

19

0

0

\[\begin{bmatrix} {+ 1} & {- j} & {- 1} & {+ j} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

20

1

2

\[\begin{bmatrix} {+ 1} & {+ j} & {- 1} & {- j} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

21

1

2

\[\begin{bmatrix} {+ 1} & {- j} & {- 1} & {+ j} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

22

2

4

\[\begin{bmatrix} {+ 1} & {+ j} & {- 1} & {- j} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

23

2

4

\[\begin{bmatrix} {+ 1} & {- j} & {- 1} & {+ j} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

 

Table 6.4.1.1.3-3: PUSCH DM-RS positions \(\overline{l}\) within a slot for single-symbol DM-RS and intra-slot frequency hopping disabled.

\(\mathbf{l}_{\text{d}}\) in symbols

DM-RS positions \(\overline{l}\)

PUSCH mapping type A

PUSCH mapping type B

dmrs-AdditionalPosition

dmrs-AdditionalPosition

pos0

pos1

pos2

pos3

pos0

pos1

pos2

pos3

<4

-

-

-

-

\(\ell_0\)

\(\ell_0\)

\(\ell_0\)

\(\ell_0\)

4

\(\ell_0\)

\(\ell_0\)

\(\ell_0\)

\(\ell_0\)

\(\ell_0\)

\(\ell_0\)

\(\ell_0\)

\(\ell_0\)

5

\(\ell_0\)

\(\ell_0\)

\(\ell_0\)

\(\ell_0\)

\(\ell_0\)

\(\ell_0\), 4

\(\ell_0\), 4

\(\ell_0\), 4

6

\(\ell_0\)

\(\ell_0\)

\(\ell_0\)

\(\ell_0\)

\(\ell_0\)

\(\ell_0\), 4

\(\ell_0\), 4

\(\ell_0\), 4

7

\(\ell_0\)

\(\ell_0\)

\(\ell_0\)

\(\ell_0\)

\(\ell_0\)

\(\ell_0\), 4

\(\ell_0\), 4

\(\ell_0\), 4

8

\(\ell_0\)

\(\ell_0\), 7

\(\ell_0\), 7

\(\ell_0\), 7

\(\ell_0\)

\(\ell_0\), 6

\(\ell_0\), 3, 6

\(\ell_0\), 3, 6

9

\(\ell_0\)

\(\ell_0\), 7

\(\ell_0\), 7

\(\ell_0\), 7

\(\ell_0\)

\(\ell_0\), 6

\(\ell_0\), 3, 6

\(\ell_0\), 3, 6

10

\(\ell_0\)

\(\ell_0\), 9

\(\ell_0\), 6, 9

\(\ell_0\), 6, 9

\(\ell_0\)

\(\ell_0\), 8

\(\ell_0\), 4, 8

\(\ell_0\), 3, 6, 9

11

\(\ell_0\)

\(\ell_0\), 9

\(\ell_0\), 6, 9

\(\ell_0\), 6, 9

\(\ell_0\)

\(\ell_0\), 8

\(\ell_0\), 4, 8

\(\ell_0\), 3, 6, 9

12

\(\ell_0\)

\(\ell_0\), 9

\(\ell_0\), 6, 9

\(\ell_0\), 5, 8, 11

\(\ell_0\)

\(\ell_0\), 10

\(\ell_0\), 5, 10

\(\ell_0\), 3, 6, 9

13

\(\ell_0\)

\(\ell_0\), 11

\(\ell_0\), 7, 11

\(\ell_0\), 5, 8, 11

\(\ell_0\)

\(\ell_0\), 10

\(\ell_0\), 5, 10

\(\ell_0\), 3, 6, 9

14

\(\ell_0\)

\(\ell_0\), 11

\(\ell_0\), 7, 11

\(\ell_0\), 5, 8, 11

\(\ell_0\)

\(\ell_0\), 10

\(\ell_0\), 5, 10

\(\ell_0\), 3, 6, 9

 

Table 6.4.1.1.3-4: PUSCH DM-RS positions \(\overline{l}\) within a slot for double-symbol DM-RS and intra-slot frequency hopping disabled.

\(l_{\text{d}}\) in symbols

DM-RS positions \(\overline{l}\)

PUSCH mapping type A

PUSCH mapping type B

dmrs-AdditionalPosition

dmrs-AdditionalPosition

pos0

pos1

pos2

pos3

pos0

pos1

pos2

pos3

<4

-

-

 

 

-

-

 

 

4

\(\ell_0\)

\(\ell_0\)

 

 

-

-

 

 

5

\(\ell_0\)

\(\ell_0\)

 

 

\(\ell_0\)

\(\ell_0\)

 

 

6

\(\ell_0\)

\(\ell_0\)

 

 

\(\ell_0\)

\(\ell_0\)

 

 

7

\(\ell_0\)

\(\ell_0\)

 

 

\(\ell_0\)

\(\ell_0\)

 

 

8

\(\ell_0\)

\(\ell_0\)

 

 

\(\ell_0\)

\(\ell_0\), 5

 

 

9

\(\ell_0\)

\(\ell_0\)

 

 

\(\ell_0\)

\(\ell_0\), 5

 

 

10

\(\ell_0\)

\(\ell_0\), 8

 

 

\(\ell_0\)

\(\ell_0\), 7

 

 

11

\(\ell_0\)

\(\ell_0\), 8

 

 

\(\ell_0\)

\(\ell_0\), 7

 

 

12

\(\ell_0\)

\(\ell_0\), 8

 

 

\(\ell_0\)

\(\ell_0\), 9

 

 

13

\(\ell_0\)

\(\ell_0\), 10

 

 

\(\ell_0\)

\(\ell_0\), 9

 

 

14

\(\ell_0\)

\(\ell_0\), 10

 

 

\(\ell_0\)

\(\ell_0\), 9

 

 

 

Table 6.4.1.1.3-5: PUSCH DM-RS time index \(\mathbf{l}\mathbf{'}\).

DM-RS multiplexing

DM-RS duration

\[\mathbf{l}\mathbf{'}\]

Supported antenna ports \(\overset{\sim}{\mathbf{p}}\)

Configuration type 1

Configuration type 2

Basic

single-symbol DM-RS

0

0 – 3

0 – 5

double-symbol DM-RS

0, 1

0 – 7

0 – 11

Enhanced

single-symbol DM-RS

0

0 – 3, 8 – 11

0 – 5, 12 – 17

double-symbol DM-RS

0, 1

0 – 15

0 – 23

 

Table 6.4.1.1.3-6: PUSCH DM-RS positions \(\overline{l}\) within a slot for single-symbol DM-RS and intra-slot frequency hopping enabled.

\(l_{\text{d}}\) in symbols

DM-RS positions \(\bar{\mathbf{l}}\)

PUSCH mapping type A

PUSCH mapping type B

\[\mathbf{l}_{0} = 0\]

\[\mathbf{l}_{0} = 2\]

\[\mathbf{l}_{0} = 3\]

dmrs-AdditionalPosition

dmrs-AdditionalPosition

dmrs-AdditionalPosition

pos0

pos1

pos0

pos1

pos0

pos1

1sthop<br>

2ndhop<br>

1sthop<br>

2ndhop<br>

1sthop<br>

2ndhop<br>

1sthop<br>

2ndhop<br>

1sthop<br>

2ndhop<br>

1sthop<br>

2ndhop<br>

≤3

-

-

-

-

-

-

-

-

0

0

\[0\]

0

4

2

0

2

0

3

0

3

0

0

0

\[0\]

0

5, 6

2

0

2

0, 4

3

0

3

0, 4

0

0

\[0,4\]

0, 4

7

2

0

2, 6

0, 4

3

0

3

0, 4

0

0

\[0,4\]

0, 4

 

6.4.1.2     Phase-tracking reference signals for PUSCH #

6.4.1.2.1     Sequence generation #
6.4.1.2.1.1     Sequence generation if transform precoding is not enabled #

If transform precoding is not enabled, the precoded phase-tracking reference signal for subcarrier \(k\) on layer \(j\) is given by

    \(r^{({\overset{\sim}{p}}_{j})}(m) = \left\{ \begin{matrix} {r(m)} & {\text{if}j = j^{'}\text{or}j = j"} \\ 0 & \text{otherwise} \end{matrix} \right.\)

where

-    antenna ports \(\tilde{p}_{j'}\) or \(\{\tilde{p}_{j'},\tilde{p}_{j''}\}\) associated with PT-RS transmission are given by clause 6.2.3 of [6, TS 38.214]

-    \(r(m)\) is given by clause 6.4.1.1.1.1

-    at the position of the first DM-RS symbol in absence of PUSCH intra-slot frequency hopping

-    at the position of the first DM-RS symbol in hop \(h \in \left\{ 0,1 \right\}\) in presence of PUSCH intra-slot frequency hopping

6.4.1.2.1.2     Sequence generation if transform precoding is enabled #

If transform precoding is enabled, the phase-tracking reference signal \(r_m(m')\) to be mapped in position \(m\) before transform precoding, where \(m\) depends on the number of PT-RS groups \(N_{\text{group}}^{\text{PT-RS}}\), the number of samples per PT-RS group \(N^{\text{group}}_{\text{samp}}\), and \(M_{\text{sc}}^{\text{PUSCH}}\) according to Table 6.4.1.2.2.2-1, shall be generated according to

\(\begin{aligned} r_m(m') &= w(k') \frac{e^{j\frac{\pi}{2}(m \bmod 2)}}{\sqrt{2}} \left[(1-2c(m')) + j(1-2c(m'))\right],\\ m' &= N_{\mathrm{samp}}^{\mathrm{group}} s' + k',\\ s' &= 0,1,\ldots, N_{\mathrm{group}}^{\mathrm{PT\text{-}RS}} - 1,\\ k' &= 0,1,\ldots, N_{\mathrm{samp}}^{\mathrm{group}} - 1. \end{aligned}\).

where the pseudo-random sequence \(c(i)\) is defined in clause 5.2.1 and \(w(i)\) is given by Table 6.4.1.2.1.2-1. The pseudo-random sequence generator shall be initialized with

    \(c_{\text{init}} = \left( {2^{17}\left( {N_{\text{symb}}^{\text{slot}}n_{\text{s,f}}^{\mu} + l + 1} \right)\left( {2N_{\text{ID}} + 1} \right) + {2N}_{\text{ID}}} \right)\text{mod}2^{31}\)

where \(l\) is the lowest OFDM symbol number in the PUSCH allocation in slot \(n_{\text{s,f}}^{\mu}\) that contains PT-RS according to clause 6.4.1.2.2.2 and \(N_{\text{ID}}\) is given by the higher-layer parameter nPUSCH-Identity.

Table 6.4.1.2.1.2-1: The orthogonal sequence \(w(i)\).

\(n_{\mathrm{RNTI}} \bmod N_{\mathrm{samp}}^{\mathrm{group}}\)

\(N^{\mathrm{group}}_{\mathrm{samp}}=2\)<br>\(\begin{bmatrix} w(0) & w(1) \end{bmatrix}\)

\(N_{\text{samp}}^{\text{group}} = 4\)<br>\(\begin{bmatrix} w(0) & w(1) & w(2) & w(3) \end{bmatrix}\)

0

\(\begin{bmatrix}+1 & +1\end{bmatrix}\)

\(\begin{bmatrix} +1 & +1 & +1 & +1 \end{bmatrix}\)

1

\(\begin{bmatrix}+1 & -1\end{bmatrix}\)

\(\begin{bmatrix}+1&-1&+1&-1\end{bmatrix}\)

2

-

\(\begin{bmatrix}+1 & +1 & -1 & -1\end{bmatrix}\)

3

-

\(\begin{bmatrix} +1 & -1 & -1 & +1 \end{bmatrix}\)

 

6.4.1.2.2     Mapping to physical resources #
6.4.1.2.2.1     Precoding and mapping to physical resources if transform precoding is not enabled #

The UE shall transmit phase-tracking reference signals only in the resource blocks used for the PUSCH, and only if the procedure in [6, TS 38.214] indicates that phase-tracking reference signals are being used.

The PUSCH PT-RS shall be mapped to resource elements according to

-    if the higher-layer parameter dmrs-TypeEnh is configured

    \(\begin{bmatrix} a_{k,l}^{({p_{o},\mu})} \\ \vdots \\ a_{k,l}^{({p_{\rho - 1},\mu})} \end{bmatrix} = \delta\beta_{\text{PT-RS}}W\begin{bmatrix} {r^{{(\overset{\sim}{p}}_{0})}(4n + k')} \\ \vdots \\ {r^{{(\overset{\sim}{p}}_{\upsilon - 1})}(4n + k')} \end{bmatrix}\)

    \(k = \begin{cases} {8n + 2k^{'} + \Delta} & \text{configuration type 1} \\ {12n + k^{'} + \Delta} & {\text{configuration type 2,}k' \in \left\{ {0,1} \right\}} \\ {12n + k^{'} + \Delta + 4} & {\text{configuration type 2,}k' \in \left\{ {2,3} \right\}} \end{cases}\)

-    otherwise

    \(\begin{bmatrix} a_{k,l}^{({p_{o},\mu})} \\ \vdots \\ a_{k,l}^{({p_{\rho - 1},\mu})} \end{bmatrix} = \delta\beta_{\text{PT-RS}}W\begin{bmatrix} {r^{{(\overset{\sim}{p}}_{0})}(2n + k')} \\ \vdots \\ {r^{{(\overset{\sim}{p}}_{\upsilon - 1})}(2n + k')} \end{bmatrix}\)

\[k = \left\{ \begin{matrix} {4n + 2k^{'} + \Delta} & {configurationtype1} \\ {6n + k^{'} + \Delta} & {configurationtype2} \end{matrix} \right.\]

when all the following conditions are fulfilled

-    \(l\) is within the OFDM symbols allocated for the PUSCH transmission

-    resource element \(\left( {k,l} \right)\) is not used for DM-RS

-    \(k'\) and \(\Delta\) correspond to \({\overset{\sim}{p}}_{0},\ldots,{\overset{\sim}{p}}_{\nu - 1}\)

The quantities \(k'\) and \(\Delta\) are given by Tables 6.4.1.1.3-1 and 6.4.1.1.3-2, the configuration type is given by the higher-layer parameter dmrs-Type in the DMRS-UplinkConfig IE, and the precoding matrix \(W\) is given by clause 6.3.1.5. The quantity \(\beta_{\text{PT-RS}}\) is an amplitude scaling factor to conform with the transmit power specified in clause 6.2.3 of [6, TS 38.214]. The quantity \(\delta = \sqrt[{}]{2}\) if \(l\) corresponds to an OFDM symbol occupied by a muting resource, otherwise \(\delta = 1\).

The set of time indices \(l\) defined relative to the start of the PUSCH allocation is defined by

1. set \(i = 0\)and \(l_{\text{ref}} = 0\)

2. if any symbol in the interval \(\max\left( {l_{\text{ref}} + \left( {i - 1} \right)L_{\text{PT-RS}} + 1,l_{\text{ref}}} \right),\ldots,l_{\text{ref}} + iL_{\text{PT-RS}}\) overlaps with a symbol used for DM-RS according to clause 6.4.1.1.3

-    set \(i = 1\)

-    set \(l_{\text{ref}}\) to the symbol index of the DM-RS symbol in case of a single-symbol DM-RS or to the symbol index of the second DM-RS symbol in case of a double-symbol DM-RS

-    repeat from step 2 as long as \(l_{\text{ref}} + iL_{\text{PT-RS}}\) is inside the PUSCH allocation

3. add \(l_{\text{ref}} + iL_{\text{PT-RS}}\) to the set of time indices for PT-RS

4. increment \(i\) by one

5. repeat from step 2 above as long as \(l_{\text{ref}} + iL_{\text{PT-RS}}\) is inside the PUSCH allocation

where \(L_{\text{PT-RS}} \in \left\{ {1,2,4} \right\}\) is defined in Table 6.2.3.1-1 of [6, TS 38.214].

For the purpose of PT-RS mapping, the resource blocks allocated for PUSCH transmission are numbered from 0 to \(N_{RB}-1\) from the lowest scheduled resource block to the highest. The corresponding subcarriers in this set of resource blocks are numbered in increasing order starting from the lowest frequency from 0 to \(N_{\text{sc}}^{\text{RB}}N_{\text{RB}} - 1\). The subcarriers to which the PT-RS shall be mapped are given by

\(k = k_{\mathrm{ref}}^{\mathrm{RE}} + \bigl(i K_{\mathrm{PT\!-\!RS}} + k_{\mathrm{ref}}^{\mathrm{RB}}\bigr) N_{\mathrm{sc}}^{\mathrm{RB}} k_{\mathrm{ref}}^{\mathrm{RB}} = \begin{cases} n_{\mathrm{RNTI}} \bmod K_{\mathrm{PT\!-\!RS}}, & \text{if } N_{\mathrm{RB}} \bmod K_{\mathrm{PT\!-\!RS}} = 0, \\ n_{\mathrm{RNTI}} \bmod \bigl(N_{\mathrm{RB}} \bmod K_{\mathrm{PT\!-\!RS}}\bigr), & \text{otherwise} \end{cases}\)

where

-    \(i=0,1,2,\ldots\)

-    \(k_{\mathrm{ref}}^{\mathrm{RE}}\) is given by Table 6.4.1.2.2.1-1 for the DM-RS port associated with the PT-RS port according to clause 6.2.3 in [6, TS 38.214]. If the higher-layer parameter resourceElementOffset in PTRS-UplinkConfig is not configured, the column corresponding to 'offset00' shall be used.

-    \(n_{\mathrm{RNTI}}\)is the RNTI associated with the DCI scheduling the transmission using C-RNTI, CS-RNTI, MCS-C-RNTI, SP-CSI-RNTI, or is the CS-RNTI in case of configured grant

-    \(N_{\text{RB}}\) is the number of resource blocks scheduled

-    \(K_{\text{PT-RS}} \in \left\{ 2,4 \right\}\) is given by [6, TS 38.214].

Table 6.4.1.2.2.1-1: The parameter \(k_{\mathrm{ref}}^{\mathrm{RE}}\) .

DM-RS antenna port

<br>\(\tilde{p}\)

\(k_{\mathrm{ref}}^{\mathrm{RE}}\)

DM-RS Configuration type 1

DM-RS Configuration type 2

resourceElementOffset

resourceElementOffset

offset00

offset01

offset10

offset11

offset00

offset01

offset10

offset11

0

0

2

6

8

0

1

6

7

1

2

4

8

10

1

6

7

0

2

1

3

7

9

2

3

8

9

3

3

5

9

11

3

8

9

2

4

-

-

-

-

4

5

10

11

5

-

-

-

-

5

10

11

4

8

4

6

10

0

-

-

-

-

9

6

8

0

2

-

-

-

-

10

5

7

11

1

-

-

-

-

11

7

9

1

3

-

-

-

-

12

-

-

-

-

6

7

0

1

13

-

-

-

-

7

0

1

6

14

-

-

-

-

8

9

2

3

15

-

-

-

-

9

2

3

8

16

-

-

-

-

10

11

4

5

17

-

-

-

-

11

4

5

10

 

6.4.1.2.2.2     Mapping to physical resources if transform precoding is enabled #

The UE shall transmit phase-tracking reference signals only in the resource blocks and OFDM symbols used for the PUSCH, and only if the procedure in [6, TS 38.214] indicates that phase-tracking reference signals are being used.

The sequence \(r_m(m')\) shall be multiplied by \(\beta'\) and mapped to \(N_{\text{samp}}^{\text{group}}N_{\text{group}}^{\text{PT-RS}}\) complex valued symbols in \(\tilde{x}^{(0)}(m)\) where

-    \(\tilde{x}^{(0)}(m)\) are the complex-valued symbols in OFDM symbol \(l\) before transform precoding according to clause 6.3.1.4

-    \(m\) depends on the number of PT-RS groups \(N_{\text{group}}^{\text{PT-RS}}\), the number of samples per PT-RS group \(N^{\text{group}}_{\text{samp} }\), and \(M_{sc}^{\mathrm{PUSCH}}\) according to Table 6.4.1.2.2.2-1

-    \(\beta'\) is the ratio between amplitude of one of the outermost constellation points for the modulation scheme used for PUSCH and one of the outermost constellation points for π/2-BPSK as defined in clause 6.2.3 of [TS 38.214]

The set of time indices \(l\) for which PT-RS shall be transmitted is defined relative to the start of the PUSCH allocation and is defined by

1. set \(i=0\) and \(l_{\mathrm{ref}}=0\)

2. if any symbol in the interval \(\max\left( {l_{\text{ref}} + \left( {i - 1} \right)L_{\text{PT-RS}} + 1,l_{\text{ref}}} \right),\ldots,l_{\text{ref}} + iL_{\text{PT-RS}}\) overlaps with a symbol used for DM-RS according to clause 6.4.1.1.3

-    set \(i = 1\)

-    set \(l_{\mathrm{ref}}\) to the symbol index of the DM-RS symbol in case of a single-symbol DM-RS and to the symbol index of the second DM-RS symbol in case of a double-symbol DM-RS

-    repeat from step 2 as long as \(l_{\mathrm{ref}} + iL_{\mathrm{PT\text{-}RS}}\) is inside the PUSCH allocation

3. add \(l_{\mathrm{ref}} + iL_{\mathrm{PT\text{-}RS}}\) to the set of time indices for PT-RS

4. increment \(i\) by one

5. repeat from step 2 above as long as \(l_{\mathrm{ref}} + iL_{\mathrm{PT\text{-}RS}}\) is inside the PUSCH allocation

where \(L_{\text{PT-RS}} \in \left\{ 1,2 \right\}\)\(L_{PT - \text{RS}} \in \left\{ 1,2 \right\}\) is given by the higher-layer parameter timeDensityTransformPrecoding in the PTRS-UplinkConfig IE.

Table 6.4.1.2.2.2-1: PT-RS symbol mapping.

Number of PT-RS groups<br><br>\(N_{\text{group}}^{\text{PT-RS}}\)

Number of samples per PT-RS group<br>\(N^{\text{group}}_{\text{samp} }\)

Index \(\mathbf{m}\) of PT-RS samples in OFDM symbol \(l\) prior to transform precoding

2

2

\(s\left\lfloor {M_{\text{sc}}^{\text{PUSCH}}/4} \right\rfloor + k - 1\) where \(s = 1,3\) and \(k = 0,1\)

 

2

4

\(sM_{\text{sc}}^{\text{PUSCH}} + k\) where \(\left\{ \begin{matrix} {s = 0} & \text{and} & {k = 0,1,2,3} \\ {s = 1} & \text{and} & {k = - 4, - 3, - 2, - 1} \end{matrix} \right.\)

 

4

2

Image \(\left\lfloor {s{M_{\text{sc}}^{\text{PUSCH}}/8}} \right\rfloor + k - 1\) where \(s = 1,3,5,7\) and \(k = 0,1\)

4

4

\({{sM}_{\text{sc}}^{\text{PUSCH}}/4} + n + k\) where \(\left\{ \begin{array}{llll} {s = 0} & \text{and} & {k = 0,1,2,3} & {n = 0} \\ {s = 1,2} & \text{and} & {k = - 2, - 1,0,1} & {n = \left\lfloor {M_{\text{sc}}^{\text{PUSCH}}/8} \right\rfloor} \\ {s = 4} & \text{and} & {k = - 4, - 3, - 2, - 1} & {n = 0} \end{array} \right.\)

 

8

4

\(\left\lfloor {s{M_{\text{sc}}^{\text{PUSCH}}/8}} \right\rfloor + n + k\) where \(\left\{ \begin{array}{llll} {s = 0} & \text{and} & {k = 0,1,2,3} & {n = 0} \\ {s = 1,2,3,4,5,6} & \text{and} & {k = - 2, - 1,0,1} & {n = \left\lfloor {M_{\text{sc}}^{\text{PUSCH}}/16} \right\rfloor} \\ {s = 8} & \text{and} & {k = - 4, - 3, - 2, - 1} & {n = 0} \end{array} \right.\)

 

 

6 .4.1.3    Demodulation reference signal for PUCCH #

6.4.1.3.1     Demodulation reference signal for PUCCH format 1 #
6.4.1.3.1.1     Sequence generation #

The reference signal sequence is defined by

zm'NSF,0PUCCH,1MRBPUCCH,1NscRB+mMRBPUCCH,1NscRB+n=wimru,vα,δnn=0,1,,MRBPUCCH,1NscRB-1m=0,1,, NSF,m'PUCCH,1-1m'=0no intra-slot frequency hopping0,1intra-slot frequency hopping

where \(N_{\text{SF},m^{'}}^{\text{PUCCH,1}}\) is given by Table 6.4.1.3.1.1-1, \(M_{\text{RB}}^{\text{PUCCH},1}\) by clause 9.2.1 of [5, TS 38.213], and the sequence \(r_{u,v}^{({\alpha,\delta})}(n)\) is given by clause 5.2.2.

Intra-slot frequency hopping shall be assumed when the higher-layer parameter intraSlotFrequencyHopping is enabled, regardless of whether the frequency-hop distance is zero or not, otherwise no intra-slot frequency hopping shall be assumed.

The orthogonal sequence \(w_i(m)\) is given by Table 6.3.2.4.1.-2 with the same index \(i\) as used in clause 6.3.2.4.1.

Table 6.4.1.3.1.1-1: Number of DM-RS symbols and the corresponding \(N^{\mathrm{PUCCH},1}_{\mathrm{SF},m'}\).

PUCCH length, <br>\(N_{\mathrm{symb}}^{\mathrm{PUCCH,1}}\)

\(N^{\mathrm{PUCCH},1}_{\mathrm{SF},m'}\)

No intra-slot hopping

\(m' = 0\)

Intra-slot hopping

\(m' = 0\)

\(m'=1\)

4

2

1

1

5

3

1

2

6

3

2

1

7

4

2

2

8

4

2

2

9

5

2

3

10

5

3

2

11

6

3

3

12

6

3

3

13

7

3

4

14

7

4

3

 

6.4.1.3.1.2     Mapping to physical resources #

The sequence shall be multiplied with the amplitude scaling factor \(\beta_{\mathrm{PUCCH},1}\) in order to conform to the transmit power specified in [5, 38.213] and mapped in sequence starting with \(z(0)\) to resource elements \(\left( {k,l} \right)_{p,\mu}\) in a slot on antenna port \(p=2000\) according to

\[\begin{matrix} {a_{k,l}^{(p,\mu)} = \beta_{\text{PUCCH,1}}z(m)} \\ {l = 0,2,4,\ldots} \end{matrix}\]

where \(l = 0\) corresponds to the first OFDM symbol of the PUCCH transmission and \(\left( {k,l} \right)_{p,\mu}\) shall be within the resource blocks assigned for PUCCH transmission according to [5, TS 38.213].

For interlaced transmission, the mapping operation shall be repeated for each resource block in the interlace and in the active bandwidth part over the assigned physical resource blocks according to clause 9.2.1 of [5, TS 38.213], with the resource-block dependent sequence generated according to clause 6.3.2.2.

6.4.1.3.2     Demodulation reference signal for PUCCH format 2 #
6.4.1.3.2.1     Sequence generation #

The reference-signal sequence \(z_{l}(m)\) shall be generated according to

\[\begin{matrix} {z_{l}\left( {mN_{\text{SF}}^{\text{PUCCH,}2} + i} \right) = w_{n}(i)r_{l}(m)} \\ {r_{l}(m) = \frac{1}{\sqrt[{}]{2}}\left( {1 - 2c\left( {2m} \right)} \right) + j\frac{1}{\sqrt[{}]{2}}\left( {1 - 2c\left( {2m + 1} \right)} \right)} \\ {i = 0,1,\ldots,N_{\text{SF}}^{\text{PUCCH,2}} - 1} \\ {m = 0,1,\ldots} \end{matrix}\]

where the pseudo-random sequence \(c(i)\) is defined in clause 5.2. The pseudo-random sequence generator shall be initialized with

    \(c_{\text{init}} = \left( {2^{17}\left( {N_{\text{symb}}^{\text{slot}}n_{\text{s,f}}^{\mu} + l + 1} \right)\left( {2N_{\text{ID}}^{0} + 1} \right) + 2N_{\text{ID}}^{0}} \right)\text{mod}2^{31}\)

where \(l\) is the OFDM symbol number within the slot, \(n_{\text{s,f}}^{\mu}\) is the slot number within the radio frame, and \(w_{n}(i)\) and \(N_{\text{SF}}^{\text{PUCCH,}2}\) are defind in clause 6.3.2.5.2A.

The quantity \(N_{\text{ID}}^{0} \in \left\{ {0,1,\ldots,65535} \right\}\) is given by the higher-layer parameter scramblingID0 in the DMRS-UplinkConfig IE if provided and by \(N_{\text{ID}}^{\text{cell}}\) otherwise. If a UE is configured with both dmrs-UplinkForPUSCH-MappingTypeA and dmrs-UplinkForPUSCH-MappingTypeB, scramblingID0 is obtained from dmrs-UplinkForPUSCH-MappingTypeB.

6.4.1.3.2.2     Mapping to physical resources #

The sequence shall be multiplied with the amplitude scaling factor \(\beta_{\text{PUCCH,2}}\) in order to conform to the transmit power specified in [5, 38.213] and mapped in sequence starting with \(z_{l}(0)\) to resource elements \(\left( {k,l} \right)_{p,\mu}\) in a slot on antenna port \(p=2000\) according to

    \(a_{k,l}^{({p,\mu})}{} = \beta_{\text{PUCCH,2}}z_{l}(m)\)    \(k{} = 3m + 1\)

where \(k\) is defined relative to subcarrier 0 of common resource block 0 and \(\left( {k,l} \right)_{p,\mu}\) shall be within the resource blocks assigned for PUCCH transmission according to clause 9.2.1 of [5, TS 38.213].

6.4.1.3.3     Demodulation reference signal for PUCCH formats 3 and 4 #
6.4.1.3.3.1     Sequence generation #

The reference-signal sequence \(r_{l}(m)\) shall be generated according to

\(\begin{aligned} r_l(m) &= r_{u,v}^{(\alpha,\delta)}(m)\\ m &= 0,1,\ldots, M_{sc}^{\mathrm{PUCCH},s} - 1 \end{aligned}\)

where \(M_{\text{sc}}^{\text{PUCCH},s}\) is given by clause 6.3.2.6.3 and \(r_{u,v}^{({\alpha,\delta})}(m)\) depends on the configuration:

-    if the higher-layer parameter dmrs-UplinkTransformPrecodingPUCCH is configured, and \(\pi/2\)-BPSK is used for PUCCH, \(r_{u,v}^{({\alpha,\delta})}(m)\) is given by clause 5.2.3 with \(\delta = 0\) and \(c_{\text{init}}\) given by clause 6.4.1.3.2.1. The sequence group \(u\) and the sequence number \(v\) depend on the sequence hopping in clause 6.3.2.2.1.

-    otherwise, for PUCCH format 3, PUCCH format 4 with \(M_{\text{RB}}^{\text{PUCCH,}4}\)=1, and PUCCH format 4 with \(M_{\text{RB}}^{\text{PUCCH,}4}\)>1 when \(\pi/2\)-BPSK is not used for PUCCH, \(r_{u,v}^{({\alpha,\delta})}(m)\) is given by clause 6.3.2.2 and the cyclic shift \(\alpha\) varies with the symbol number and slot number according to clause 6.3.2.2.2 with

-    \(m_{0} = 0\) for PUCCH format 3 without interlaced mapping;

-    \(m_{0}\) obtained from Table 6.4.1.3.3.1-1 with the orthogonal sequence index \(n\) given by clause 6.3.2.6.3 for PUCCH format 3 with interlaced mapping and PUCCH format 4.

 

Table 6.4.1.3.3.1-1: Cyclic shift index \(\mathbf{m}_{0}\) for PUCCH format 3 with interlaced mapping and PUCCH format 4.

Orthogonal sequence index \(\mathbf{n}\)

Cyclic shift index \(m_0\)

\[\mathbf{N}_{\text{SF}}^{\text{PUCCH,}\mathbf{s}} = 1\]

\[\mathbf{N}_{\text{SF}}^{\text{PUCCH,}\mathbf{s}} = 2\]

\[\begin{matrix} \\ {\mathbf{N}_{\text{SF}}^{\text{PUCCH,}\mathbf{s}} = 4} \end{matrix}\]

0

0

0

0

1

-

6

6

2

-

-

3

3

-

-

9

 

6.4.1.3.3.2     Mapping to physical resources #

The sequence shall be multiplied with the amplitude scaling factor \(\beta_{\mathrm{PUCCH},s}\), \(s \in \{3,4\}\), in order to conform to the transmit power specified in [5, 38.213] and mapped in sequence starting with \(r_l(0)\) to resource elements \(\left( {k,l} \right)_{p,\mu}\) on antenna port \(p=2000\) according to

\(\begin{aligned} a_{k,l}^{(p,\mu)} &= \beta_{\mathrm{PUCCH},s}\cdot r_l(m).\\ m &= 0,1,\ldots,M_{sc}^{\mathrm{PUCCH},s}-1 \end{aligned}\)

where

-    \(k\) is defined relative to subcarrier 0 of the lowest-numbered resource block assigned for PUCCH transmission,

-    \(l\) is given by Table 6.4.1.3.3.2-1 for the case with and without intra-slot frequency hopping and with and without additional DM-RS as described in clause 9.2.1 of [TS 38.213], where \(l=0\) corresponds to the first OFDM symbol of the PUCCH transmission.

The resource elements \(\left( {k,l} \right)_{p,\mu}\) shall be within the resource blocks assigned for PUCCH transmission according to clause 9.2.1 of [5, TS 38.213].

Table 6.4.1.3.3.2-1: DM-RS positions for PUCCH format 3 and 4.

PUCCH length

DM-RS position \(l\) within PUCCH span

No additional DM-RS

Additional DM-RS

No hopping

Hopping

No hopping

Hopping

4

1

0, 2

1

0, 2

5

0, 3

0, 3

6

1, 4

1, 4

7

1, 4

1, 4

8

1, 5

1, 5

9

1, 6

1, 6

10

2, 7

1, 3, 6, 8

11

2, 7

1, 3, 6, 9

12

2, 8

1, 4, 7, 10

13

2, 9

1, 4, 7, 11

14

3, 10

1, 5, 8, 12

 

6 .4.1.4    Sounding reference signal #

6.4.1.4.1     SRS resource #

An SRS resource is configured by the SRS-Resource IE or the SRS-PosResource IE and consists of

-    \(N_{\text{ap}}^{\text{SRS}} \in \left\{ {1,2,4,8} \right\}\) antenna ports \(\left\{ p_{i} \right\}_{i = 0}^{N_{\text{ap}}^{\text{SRS}} - 1}\), where the number of antenna ports is given by the higher layer parameter nrofSRS-Ports or nrofSRS-Ports-n8 if configured, otherwise \(N_{\text{ap}}^{\text{SRS}} = 1\), and \(p_{i} = 1000 + i\) when the SRS resource is in a SRS resource set with higher-layer parameter usage in SRS-ResourceSet not set to 'nonCodebook', or determined according to [6, TS 38.214] when the SRS resource is in a SRS resource set with higher-layer parameter usage in SRS-ResourceSet set to 'nonCodebook'.

-    \(N_{\text{hop}}\), the number of hops for SRS Tx hopping for an SRS resource configured by SRS-PosResource and given by the higher layer parameter numberOfHops if configured, otherwise \(N_{\text{hop}} = 1\).

-    \(N_{\text{symb}}^{\text{SRS}} \in \left\{ {1,2,4,8,10,12,14} \right\}\) consecutive OFDM symbols given by the field nrofSymbols contained in the higher layer parameter resourceMapping. If \(N_{\text{hop}} > 1\), \(N_{\text{symb}}^{\text{SRS}}\) is the number of consecutive OFDM symbol per hop.

-    \(l_{0}\), the starting position in the time domain given by \(l_{0} = N_{\text{symb}}^{\text{slot}} - 1 - l_{\text{offset}}\) where the offset \(l_{\text{offset}} \in \left\{ {0,1,\ldots,13} \right\}\) counts symbols backwards from the end of the slot and is given by the field startPosition contained in the higher layer parameter resourceMapping and \(l_{\text{offset}} \geq N_{\text{symb}}^{\text{SRS}} - 1\). If \(N_{\text{hop}} > 1\) \(l_{0}\) is the starting position of each hop in the time domain, determined by the field startPosition for each SRS transmission hop.

-    \(k_{0}\), the frequency-domain starting position of the sounding reference signal.

6.4.1.4. 2    Sequence generation #

The sounding reference signal sequence for an SRS resource, or if numberOfHops for SRS-PosResource is provided, for a given hop within an SRS resource, shall be generated according to

    \(r^{(p_{i})}\left( {n,l'} \right) = w_{\text{TDM}}^{(p_{i})}\left( {l'} \right)r_{u,v}^{(\alpha_{i},\delta)}(n)\)

    \(0 \leq n \leq M_{\text{sc},b}^{\text{SRS}} - 1\)

    \(l' \in \left\{ {0,1,\ldots,N_{\text{symb}}^{\text{SRS}} - 1} \right\}\)

where \(M_{\text{sc},b}^{\text{SRS}}\) is given by clause 6.4.1.4.3, \(r_{u,v}^{({\alpha,\delta})}(n)\) is given by clause 5.2.2 with \(\delta = \log_{\text{2}}\left( K_{\text{TC}} \right)\) and the transmission comb number \(K_{\text{TC}} \in \left\{ {2,4,8} \right\}\) is contained in the higher-layer parameter transmissionComb. The quantity \(l' \in \left\{ {0,1,\ldots,N_{\text{symb}}^{\text{SRS}} - 1} \right\}\) is the OFDM symbol number within the SRS resource.

The quantity \(w_{\text{TDM}}^{(p_{i})}\left( l^{'} \right)\) is given by

-    if the higher-layer parameter nrofSRS-Ports-n8 equals ports8tdm

\[w_{\text{TDM}}^{(p_{i})}\left( l^{'} \right) = \left\{ \begin{matrix} 1 & {\text{if}l' \in \left\{ {0,2,\ldots,N_{\text{symb}}^{\text{SRS}} - 2} \right\}\text{and}p_{i} \in \left\{ 1000,1001,1004,1005 \right\}} \\ 1 & {\text{if}l' \in \left\{ {1,3,\ldots,N_{\text{symb}}^{\text{SRS}} - 1} \right\}\text{and}p_{i} \in \left\{ 1002,1003,1006,1007 \right\}} \\ 0 & \text{otherwise} \end{matrix} \right.\]

-    otherwise

\[w_{\text{TDM}}^{(p_{i})}\left( l^{'} \right) = 1\]

The cyclic shift \(\alpha_{i}\) for antenna port \(p_{i}\) is given as

\[\alpha_{i} = 2\pi\left( {\frac{n_{\text{SRS}}^{\text{cs},i}}{n_{\text{SRS}}^{\text{cs},\max}} + \frac{f_{\text{csh}}\left( {{n_{f},n}_{\text{s,f}}^{\mu},l^{'}} \right)}{{Kn}_{\text{SRS}}^{\text{cs},\max}}} \right)\]

where

\[n_{\text{SRS}}^{\text{cs},i} = \begin{cases} {\left( {n_{\text{SRS}}^{\text{cs}} + \frac{n_{\text{SRS}}^{\text{cs},\max}\left\lfloor {\left( {{\bar{p}}_{i} - 1000} \right)/4} \right\rfloor}{{\bar{N}}_{\text{ap}}^{\text{SRS}}/4}} \right)\text{mod}n_{\text{SRS}}^{\text{cs},\max}} & {\text{if}{\bar{N}}_{\text{ap}}^{\text{SRS}} = 8\text{and}n_{\text{SRS}}^{\text{cs,max}} = 6} \\ {\left( {n_{\text{SRS}}^{\text{cs}} + \frac{n_{\text{SRS}}^{\text{cs},\max}\left\lfloor {\left( {{\bar{p}}_{i} - 1000} \right)/2} \right\rfloor}{{\bar{N}}_{\text{ap}}^{\text{SRS}}/2}} \right)\text{mod}n_{\text{SRS}}^{\text{cs},\max}} & {\text{if}{\bar{N}}_{\text{ap}}^{\text{SRS}} = 4\text{and}n_{\text{SRS}}^{\text{cs},\max}\text{=6; or if}{\bar{N}}_{\text{ap}}^{\text{SRS}} = 8\text{and}n_{\text{SRS}}^{\text{cs},\max}\text{=12}} \\ {\left( {n_{\text{SRS}}^{\text{cs}} + \frac{n_{\text{SRS}}^{\text{cs},\max}\left( {{\bar{p}}_{i} - 1000} \right)}{{\bar{N}}_{\text{ap}}^{\text{SRS}}}} \right)\text{mod}n_{\text{SRS}}^{\text{cs},\max}} & \text{otherwise} \end{cases}\]

where \(n_{\text{SRS}}^{\text{cs}} \in \left\{ {0,1,\ldots,n_{\text{SRS}}^{\text{cs},\max} - 1} \right\}\) is contained in the higher layer parameter transmissionComb. The maximum number of cyclic shifts \(n_{\text{SRS}}^{\text{cs,max}}\) is given by Table 6.4.1.4.2-1.

The quantities \({\bar{p}}_{i}\) and \({\bar{N}}_{\text{ap}}^{\text{SRS}}\) are given by

-    if the higher-layer parameter nrofSRS-Ports-n8 equals ports8tdm

pi=1000+pi mod 2if pi-1000<4 1000+pi mod 2+2if pi-10004NapSRS=4

-    otherwise

\[\begin{matrix} {{\bar{p}}_{i} = p_{i}} \\ {{\bar{N}}_{\text{ap}}^{\text{SRS}} = N_{\text{ap}}^{\text{SRS}}} \end{matrix}\]

The quantity \(f_{\text{csh}}\left( {n_{f},n_{\text{s,f}}^{\mu},l^{'}} \right)\) is given by

-    if the higher-layer parameter cyclicShiftHopping is not configured:

\[f_{\text{csh}}\left( {{n_{f},n}_{\text{s,f}}^{\mu},l^{'}} \right) = 0\]

-    if the higher-layer parameter cyclicShiftHopping is configured:

\[\begin{matrix} {f_{\text{csh}}\left( {n_{f},n_{\text{s,f}}^{\mu},l^{'}} \right) =} \\ {s_{\text{csh}}^{\text{SRS}}\left( {\left( {\sum_{m = 0}^{7}\left( {c\left( {8\left( {\left( {n_{f}mod128} \right)N_{\text{slot}}^{frame,\mu}N_{\text{symb}}^{\text{slot}} + n_{s,f}^{\mu}N_{\text{symb}}^{\text{slot}} + l_{0} + l'} \right) + m} \right)2^{m}} \right)} \right)\text{mod}n_{\text{csh}}^{\text{SRS}}} \right)} \end{matrix}\]

    where \(s_{\text{csh}}^{\text{SRS}}(n)\) and \(n_{\text{csh}}^{\text{SRS}}\)is the \((n + 1)\)th entry and the cardinality of the set

\[\mathcal{S}_{\text{csh}} = \left\{ s_{\text{csh}}^{\text{SRS}}(0),{s_{\text{csh}}^{\text{SRS}}(1),\ldots,s}_{\text{csh}}^{\text{SRS}}\left( {n_{\text{csh}}^{\text{SRS}} - 1} \right) \right\}\]

    respectively, where \(\mathcal{S}_{\text{csh}}\) is given by the higher-layer parameter hoppingSubset in the cyclicShiftHopping IE if configured, otherwise \(\mathcal{S}_{\text{csh}} = \left\{ 0,1,\ldots,Kn_{SRS}^{cs,\max} - 1 \right\}\). The higher-layer parameter hoppingSubset in the cyclicShiftHopping IE includes a bitmap of \(n_{\text{SRS}}^{\text{cs,max}}\) bits with \(1 < n_{\text{csh}}^{\text{SRS}} < n_{\text{SRS}}^{\text{cs,max}}\) non-zero bits, where if the \((n + 1)\)th non-zero bit is the \(t\):th bit in the bitmap, then \(s_{\text{csh}}^{\text{SRS}}(n) = t - 1\).

    The pseudo-random sequence \(c(i)\) is defined by clause 5.2.1 and shall be initialized with \(c_{\text{init}} = n_{\text{ID}}^{\text{hop}}\) at the beginning of each radio frame for which \(n_{f}mod128 = 0\), where the cyclic-shift hopping identity \(n_{\text{ID}}^{\text{hop}}\) is contained in the higher-layer parameter cyclicShiftHopping.

    If the higher-layer parameter hoppingFinerGranularity is configured, \(K = 2\), otherwise \(K = 1\).

The sequence group \(u = \left( {f_{\text{gh}}\left( {n_{\text{s,f}}^{\mu},l'} \right) + n_{\text{ID}}^{\text{SRS}}} \right)\text{mod}30\) and the sequence number \(v\) in clause 5.2.2 depends on the higher-layer parameter groupOrSequenceHopping in the SRS-Resource IE or the SRS-PosResource IE. The SRS sequence identity \(n_{\text{ID}}^{\text{SRS}} \in \left\{ {0,1,\ldots,65535} \right\}\) is given by the higher layer parameter sequenceId in the SRS-Resource IE.

-    if groupOrSequenceHopping equals 'neither', neither group, nor sequence hopping shall be used and

\(\[ f_{gh}\left(n_{s,f}^{\mu},\, l'\right)=0 \] \[ \nu=0 \]\)

-    if groupOrSequenceHopping equals 'groupHopping', group hopping but not sequence hopping shall be used and

\(f_{gh}\!\left(n_{s,f}^{\mu},\,l'\right)=\left(\sum_{m=0}^{7} c\!\left(8\!\left(n_{s,f}^{\mu}N_{\text{symb}}^{\text{slot}}+l_0+l'\right)+m\right)\cdot 2^{m}\right)\bmod 30 v=0\)

    where the pseudo-random sequence \(c(i)\) is defined by clause 5.2.1 and shall be initialized with \(c_{\text{init}} = n_{\text{ID}}^{\text{SRS}}\) at the beginning of each radio frame.

-    if groupOrSequenceHopping equals 'sequenceHopping', sequence hopping but not group hopping shall be used and

\(f_{gh}\!\left(n_{s,f}^{\mu},\, l'\right)=0 \nu=\begin{cases} c\!\left(n_{s,f}^{\mu}N_{\text{symb}}^{\text{slot}}+l_{0}+l'\right), & M_{sc,b}^{\text{SRS}}\ge 6\,N_{sc}^{\text{RB}},\\ 0, & \text{otherwise}. \end{cases}\)

    where the pseudo-random sequence \(c(i)\) is defined by clause 5.2.1 and shall be initialized with \(c_{\text{init}} = n_{\text{ID}}^{\text{SRS}}\) at the beginning of each radio frame.

Table 6.4.1.4.2-1: Maximum number of cyclic shifts \(\mathbf{n}_{\text{SRS}}^{\text{cs,max}}\) as a function of \(\mathbf{K}_{\text{TC}}\).

\[\mathbf{K}_{\text{TC}}\]

\[\mathbf{n}_{\text{SRS}}^{\text{cs,max}}\]

2

8

4

12

8

6

 

6.4.1.4. 3    Mapping to physical resources #

Throughout this clause, when the higher layer parameter numberOfHops is provided for SRS-PosResource, the sounding reference signal sequence definitions applies to a given hop.

When SRS is transmitted on a given SRS resource, the sequence \(r^{(p_{i})}(n,l')\) for each OFDM symbol \(l'\) and for each of the antenna ports of the SRS resource shall be multiplied with the amplitude scaling factor \(\beta_{\mathrm{SRS}}\) in order to conform to the transmit power specified in [5, 38.213] and mapped in sequence starting with \(r^{(p_i)}(0,l')\) to resource elements \((k,l)\) in a slot for each of the antenna ports \(p_i\) according to

\[a_{K_{\text{TC}}k^{'} + k_{0}^{(p_{i})},l^{'} + l_{0}}^{(p_{i})} = \begin{cases} {\frac{1}{\sqrt[{}]{{\overset{\sim}{N}}_{\text{ap}}^{\text{SRS}}}}\beta_{\text{SRS}}r^{(p_{i})}\left( k^{'},l' \right)} & {\text{if}k^{'} = 0,1,\ldots,M_{sc,b}^{\text{SRS}} - 1\text{and}l^{'} = 0,1,\ldots,N_{\text{symb}}^{\text{SRS}} - 1} \\ 0 & \text{otherwise} \end{cases}\]

where

-    for an SRS resource in an SRS resource set with the higher-layer parameter 4portSRS_3TX is configured, \({\overset{\sim}{N}}_{\text{ap}}^{\text{SRS}} = N_{\text{ap}}^{\text{SRS}} - 1\)

-    otherwise, \({\overset{\sim}{N}}_{\text{ap}}^{\text{SRS}} = N_{\text{ap}}^{\text{SRS}}\)

The length of the sounding reference signal sequence is given by

\[M_{\text{sc},b}^{\text{SRS}} = {{m_{\text{SRS},b}N_{\text{sc}}^{\text{RB}}}/\left( {K_{\text{TC}}P_{\text{F}}} \right)}\]

where \(m_{\text{SRS},b}\) is given by a selected="selected" row of Table 6.4.1.4.3-1 with \(b = B_{\mathrm{SRS}}\) where \(B_{SRS} \in \{0,1,2,3\}\) is given by the field b-SRS contained in the higher-layer parameter freqHopping if configured, otherwise \(B_{\text{SRS}} = 0\). The row of the table is selected="selected" according to the index \(C_{\mathrm{SRS}} \in \{0,1,\ldots,63\}\) given by the field c-SRS contained in the higher-layer parameter freqHopping. The quantity \(P_{\text{F}}\) \(\in \left\{ {2,4} \right\}\) is given by the higher-layer parameter FreqScalingFactor if configured, otherwise \(P_{\text{F}} = 1\). When FreqScalingFactor is configured, the UE expects the length of the SRS sequence to be a multiple="multiple" of 6.

The frequency-domain starting position \(k_{0}^{(p_{i})}\) is defined by

\[k_{0}^{(p_{i})} = {\bar{k}}_{0}^{(p_{i})} + n_{\text{offset}}^{\text{FH}} + n_{\text{offset}}^{\text{RPFS}} + n_{\text{offset2}}^{\text{FH}}\]

where

\[{\bar{k}}_{0}^{(p_{i})} = n_{\text{shift}}N_{\text{sc}}^{\text{RB}} + \left( {k_{\text{TC}}^{(p_{i})} + k_{\text{offset}}^{l^{'}} + f_{\text{coh}}\left( {n_{f},n_{\text{s,f}}^{\mu},l^{''}} \right)} \right)\text{mod}K_{\text{TC}}\]

\[k_{\text{TC}}^{(p_{i})} = \begin{cases} {\left( {{\bar{k}}_{\text{TC}} + {{3K}_{\text{TC}}/4}} \right)\text{mod}K_{\text{TC}}} & {\text{if}{\bar{N}}_{\text{ap}}^{\text{SRS}} = 8,{\bar{p}}_{i} \in \left\{ {1003,1007} \right\}\text{, and}n_{\text{SRS}}^{\text{cs,max}} = 6} \\ {\left( {{\bar{k}}_{\text{TC}} + {K_{\text{TC}}/2}} \right)\text{mod}K_{\text{TC}}} & {\text{if}{\bar{N}}_{\text{ap}}^{\text{SRS}} = 8,{\bar{p}}_{i} \in \left\{ {1002,1006} \right\}\text{, and}n_{\text{SRS}}^{\text{cs,max}} = 6} \\ {\left( {{\bar{k}}_{\text{TC}} + {K_{\text{TC}}/4}} \right)\text{mod}K_{\text{TC}}} & {\text{if}{\bar{N}}_{\text{ap}}^{\text{SRS}} = 8,{\bar{p}}_{i} \in \left\{ {1001,1005} \right\}\text{, and}n_{\text{SRS}}^{\text{cs,max}} = 6} \\ {\left( {{\bar{k}}_{\text{TC}} + {K_{\text{TC}}/2}} \right)\text{mod}K_{\text{TC}}} & {\text{if}{\bar{N}}_{\text{ap}}^{\text{SRS}} = 8,{\bar{p}}_{i} \in \left\{ {1001,1003,1005,1007} \right\}\text{, and}n_{\text{SRS}}^{\text{cs,max}} = 12} \\ {\left( {{\bar{k}}_{\text{TC}} + {K_{\text{TC}}/2}} \right)\text{mod}K_{\text{TC}}} & {\text{if}{\bar{N}}_{\text{ap}}^{\text{SRS}} = 8,{\bar{p}}_{i} \in \left\{ {1001,1003,1005,1007} \right\}\text{,}n_{\text{SRS}}^{\text{cs,max}} = 8,\text{and}n_{\text{SRS}}^{\text{cs}} \geq {n_{\text{SRS}}^{\text{cs,max}}/2}} \\ {\left( {{\bar{k}}_{\text{TC}} + {K_{\text{TC}}/2}} \right)\text{mod}K_{\text{TC}}} & {\text{if}{\bar{N}}_{\text{ap}}^{\text{SRS}} = 4,{\bar{p}}_{i} \in \left\{ {1001,1003} \right\}\text{, and}n_{\text{SRS}}^{\text{cs,max}} = 6} \\ {\left( {{\bar{k}}_{\text{TC}} + {K_{\text{TC}}/2}} \right)\text{mod}K_{\text{TC}}} & {\text{if}{\bar{N}}_{\text{ap}}^{\text{SRS}} = 4,{\bar{p}}_{i} \in \left\{ {1001,1003} \right\}\text{,}n_{\text{SRS}}^{\text{cs,max}} \in \left\{ {8,12} \right\},\text{and}n_{\text{SRS}}^{\text{cs}} \geq {n_{\text{SRS}}^{\text{cs,max}}/2}} \\ {\bar{k}}_{\text{TC}} & \text{otherwise} \end{cases}\]

\[n_{\text{offset}}^{\text{FH}} = \sum\limits_{b = 0}^{B_{\text{SRS}}}{m_{\text{SRS},b}N_{\text{sc}}^{\text{RB}}n_{b}}\]

\[n_{\text{offset}}^{\text{RPFS}} = N_{\text{sc}}^{\text{RB}}{{m_{\text{SRS},B_{\text{SRS}}}\left( {\left( {k_{\text{F}} + k_{\text{hop}}} \right)\text{mod}P_{\text{F}}} \right)}/P_{\text{F}}}\]

\[n_{\text{offset2}}^{\text{FH}} = \left( {\left( {n_{\text{init}}^{\text{hop}} + n_{\text{SRS}}^{\text{TxHopping}}} \right)\text{mod}N_{\text{hop}} - n_{\text{init}}^{\text{hop}}} \right)\left( {m_{\text{SRS},0} - m_{\text{overlap}}^{\text{hop}}} \right)N_{\text{sc}}^{\text{RB}}\]

and

-    \(k_{\text{F}} \in \left\{ {0,1,\ldots,P_{\text{F}} - 1} \right\}\) is given by the higher-layer parameter StartRBIndex if configured, otherwise \(k_{\text{F}} = 0\);

-    \(k_{\text{hop}}\) is given by Table 6.4.1.4.3-3 with

\[\begin{matrix} {{\bar{k}}_{\text{hop}} = \left\lfloor \frac{n_{\text{SRS}}}{\prod_{b' = b_{\text{hop}}}^{B_{\text{SRS}}}N_{b'}} \right\rfloor\text{mod}P_{\text{F}}} \\ {N_{b_{\text{hop}}} = 1} \end{matrix}\]

    if the higher-layer parameter enableStartRBHopping is configured, otherwise \(k_{\text{hop}} = 0\).

-    \(m_{\text{overlap}}^{\text{hop}} \in \left\{ {0,1,2,4} \right\}\) is given by the higher-layer parameter overlapValue in TxHoppingConfig.

-    \(n_{\text{SRS}}^{\text{TxHopping}} = 0,1,\ldots,N_{\text{hop}} - 1\) is the hop transmission counter in the time domain, where \(n_{\text{SRS}}^{\text{TxHopping}} = 0\) corresponds to the hop with starting symbol and slot offset configured by resourceMapping and resourceType in SRS-PosResource, \(n_{\text{SRS}}^{\text{TxHopping}} = 1,2,\ldots,N_{\text{hop}} - 1\) corresponds to the order of the higher-layer parameter SlotOffsetForRemainingHops in slotOffsetForRemainingHopsList, wherein the UE expects to be configured with the starting slot offset and starting symbol of the \(N_{\text{hop}}\) hops in an ascending order sequentially in time domain.

-    \(n_{\text{init}}^{\text{hop}} = \left\lfloor {n_{\text{shift}}/\left( {m_{\text{SRS},0} - m_{\text{overlap}}^{\text{hop}}} \right)} \right\rfloor\) is the initial hop index.

 

The quantity \(f_{\text{coh}}\left( {n_{f},n_{\text{s,f}}^{\mu},l^{''}} \right)\) is given by

-    if the higher-layer parameter combOffsetHopping is not configured:

\[f_{\text{coh}}\left( {n_{f},n_{\text{s,f}}^{\mu},l^{''}} \right) = 0\]

-    if the higher-layer parameter combOffsetHopping is configured:

\[\begin{matrix} {f_{\text{coh}}\left( {{n_{f},n}_{\text{s,f}}^{\mu},l^{''}} \right) =} \\ {s_{\text{coh}}^{\text{SRS}}\left( {\left( {\sum_{m = 0}^{7}\left( {c\left( {8\left( {\left( {n_{f}mod128} \right)N_{\text{slot}}^{frame,\mu}N_{\text{symb}}^{\text{slot}} + n_{s,f}^{\mu}N_{\text{symb}}^{\text{slot}} + l_{0} + l''} \right) + m} \right)2^{m}} \right)} \right)\text{mod}n_{\text{coh}}^{\text{SRS}}} \right)} \end{matrix}\]

    where \(s_{\text{coh}}^{\text{SRS}}(n)\) and \(n_{\text{coh}}^{\text{SRS}}\)is the \(\left( {n + 1} \right)\)th entry and the cardinality of the set

\[\mathcal{S}_{\text{coh}} = \left\{ s_{\text{coh}}^{\text{SRS}}(0),{s_{\text{coh}}^{\text{SRS}}(1),\ldots,s}_{\text{coh}}^{\text{SRS}}\left( {n_{\text{coh}}^{\text{SRS}} - 1} \right) \right\}\]

    respectively, where \(\mathcal{S}_{\text{coh}}\) is given by the higher-layer parameter hoppingSubset in the combOffsetHopping IE if configured, otherwise \(\mathcal{S}_{\text{coh}} = \left\{ 0,1,\ldots,K_{TC} - 1 \right\}\). The higher-layer parameter hoppingSubset in the combOffsetHopping IE includes a bitmap of \(K_{\text{TC}}\) bits with \(1 < n_{\text{coh}}^{\text{SRS}} < K_{\text{TC}}\) non-zero bits, where if the \((n + 1)\)th non-zero bit is the \(t\):th bit in the bitmap, then \(s_{\text{coh}}^{\text{SRS}}(n) = t - 1\).

    The pseudo-random sequence \(c(i)\) is defined by clause 5.2.1 and shall be initialized with \(c_{\text{init}} = n_{\text{ID}}^{\text{hop}}\) at the beginning of each radio frame for which \(n_{f}\text{mod}128 = 0\), where the comb offset hopping identity \(n_{\text{ID}}^{\text{hop}}\) is contained in the higher-layer parameter combOffsetHopping.

    If the higher-layer parameter hoppingWithRepetition is set to repetition, \(l^{''} = \left\lfloor {{l'}/R} \right\rfloor R\), otherwise \(l^{''} = l'\).

 

If numberOfHops is configured:

-    The reference point for \(k_{0}^{(p_{i})} = 0\) is the lowest subcarrier of the configured bandwidth for SRS with Tx hopping configured by the parameter bwp in SRS-PosTx-Hopping.

otherwise:

-    If \(N_{\text{BWP}}^{\text{start}} \leq n_{\text{shift}}\) the reference point for \(k_{0}^{(p_{i})} = 0\) is subcarrier 0 in common resource block 0, otherwise the reference point is the lowest subcarrier of the BWP.

If the SRS is configured by the IE SRS-PosResource, the quantity \(k_{\text{offset}}^{l^{'}}\) is given by Table 6.4.1.4.3-2, otherwise \(k_{\text{offset}}^{l^{'}} = 0\).

The frequency domain shift value \(n_{\text{shift}}\) adjusts the SRS allocation with respect to the reference point grid and is contained in the higher-layer parameter freqDomainShift in the SRS-Resource IE or the SRS-PosResource IE. The transmission comb offset \({\bar{k}}_{\text{TC}} \in \left\{ {0,1,\ldots,K_{\text{TC}} - 1} \right\}\) is contained in the higher-layer parameter transmissionComb in the SRS-Resource IE or the SRS-PosResource IE and \(n_{b}\) is a frequency position index.

Frequency hopping of the sounding reference signal is configured by the parameter \(b_{\text{hop}} \in \left\{ {0,1,2,3} \right\}\), given by the field b-hop contained in the higher-layer parameter freqHopping if configured, otherwise \(b_{\text{hop}} = 0\).

If \(b_{\text{hop}} \geq B_{\text{SRS}}\), frequency hopping is disabled="disabled" and the frequency position index \(n_{b}\) remains constant (unless re-configured) and is defined by

\(n_b = \left\lfloor \frac{4 n_{\mathrm{RRC}}}{m_{\mathrm{SRS},b}} \right\rfloor \bmod N_b\)

for all \(N_{\text{symb}}^{\text{SRS}}\) OFDM symbols of the SRS resource. The quantity \(n_{\mathrm{RRC}}\) is given by the higher-layer parameter freqDomainPosition if configured, otherwise \(n_{\text{RRC}} = 0\), and the values of \(m_{\text{SRS},b}\) and \(N_{\text{b}}\) for \(b = B_{\text{SRS}}\) are given by the selected="selected" row of Table 6.4.1.4.3-1 corresponding to the configured value of \(C_{\mathrm{SRS}}\).

If \(b_{\text{hop}} < B_{\text{SRS}}\), frequency hopping is enabled and the frequency position indices \(n_{b}\) are defined by

\[n_{b} = \begin{cases} {\left\lfloor {{4n_{\text{RRC}}}/m_{\text{SRS},b}} \right\rfloor\text{mod}N_{\text{b}}} & {b \leq b_{\text{hop}}} \\ {\left( {F_{b}\left( n_{\text{SRS}} \right) + \left\lfloor {{4n_{\text{RRC}}}/m_{\text{SRS},b}} \right\rfloor} \right)\text{mod}N_{\text{b}}} & \text{otherwise} \end{cases}\]

where \(N_{\text{b}}\) is given by Table 6.4.1.4.3-1,

Image

and where \(N_{b_{\text{hop}}} = 1\) regardless of the value of \(N_{\text{b}}\). The quantity \(n_{\text{SRS}}\) counts the number of SRS transmissions. For the case of an SRS resource configured as aperiodic by the higher-layer parameter resourceType, it is given by \(n_{\text{SRS}} = \left\lfloor {{l'}/\left( {sR} \right)} \right\rfloor\) within the slot in which the \(N_{\text{symb}}^{\text{SRS}}\) symbol SRS resource is transmitted. The quantity \(s\) is given by \(s = 2\) if the higher-layer parameter nrofSRS-Ports-n8 equals ‘ports8tdm’, otherwise \(s = 1\). The quantity \(R \leq {N_{\text{symb}}^{\text{SRS}}/s}\) is the repetition factor given by the field repetitionFactor if configured, otherwise \(R = N_{\text{symb}}^{\text{SRS}}\).

For the case of an SRS resource configured as periodic or semi-persistent by the higher-layer parameter resourceType, the SRS counter is given by

\[n_{\text{SRS}} = \left( \frac{N_{\text{slot}}^{frame,\mu}n_{f} + n_{s,f}^{\mu} - T_{\text{offset}}}{T_{\text{SRS}}} \right)\left( \frac{N_{\text{symb}}^{\text{SRS}}}{sR} \right) + \left\lfloor \frac{l'}{sR} \right\rfloor\]

for slots that satisfy \(\left(N_{\text{slot}}^{\text{frame},\mu} n_f + n_{s,f}^{\mu} - T_{\text{offset}}\right) \bmod T_{\text{SRS}} = 0\). The periodicity \(T_{\mathrm{SRS}}\) in slots and slot offset \(T_{\text{offset}}\) are given in clause 6.4.1.4.4.

 

Table 6.4.1.4.3-1: SRS bandwidth configuration.

\(C_{\mathrm{SRS}}\)

\(B_{\mathrm{SRS}}=0\)

\(B_{SRS}=1\)

\(B_{SRS} = 2\)

\(B_{\mathrm{SRS}}=3\)

 

\(m_{\mathrm{SRS},0}\)

\(N_0\)

\(m_{\mathrm{SRS},1}\)

\(N_{1}\)

\(m_{\mathrm{SRS},2}\)

\(N_{2}\)

\(m_{\mathrm{SRS},3}\)

\(N_3\)

0

4

1

4

1

4

1

4

1

1

8

1

4

2

4

1

4

1

2

12

1

4

3

4

1

4

1

3

16

1

4

4

4

1

4

1

4

16

1

8

2

4

2

4

1

5

20

1

4

5

4

1

4

1

6

24

1

4

6

4

1

4

1

7

24

1

12

2

4

3

4

1

8

28

1

4

7

4

1

4

1

9

32

1

16

2

8

2

4

2

10

36

1

12

3

4

3

4

1

11

40

1

20

2

4

5

4

1

12

48

1

16

3

8

2

4

2

13

48

1

24

2

12

2

4

3

14

52

1

4

13

4

1

4

1

15

56

1

28

2

4

7

4

1

16

60

1

20

3

4

5

4

1

17

64

1

32

2

16

2

4

4

18

72

1

24

3

12

2

4

3

19

72

1

36

2

12

3

4

3

20

76

1

4

19

4

1

4

1

21

80

1

40

2

20

2

4

5

22

88

1

44

2

4

11

4

1

23

96

1

32

3

16

2

4

4

24

96

1

48

2

24

2

4

6

25

104

1

52

2

4

13

4

1

26

112

1

56

2

28

2

4

7

27

120

1

60

2

20

3

4

5

28

120

1

40

3

8

5

4

2

29

120

1

24

5

12

2

4

3

30

128

1

64

2

32

2

4

8

31

128

1

64

2

16

4

4

4

32

128

1

16

8

8

2

4

2

33

132

1

44

3

4

11

4

1

34

136

1

68

2

4

17

4

1

35

144

1

72

2

36

2

4

9

36

144

1

48

3

24

2

12

2

37

144

1

48

3

16

3

4

4

38

144

1

16

9

8

2

4

2

39

152

1

76

2

4

19

4

1

40

160

1

80

2

40

2

4

10

41

160

1

80

2

20

4

4

5

42

160

1

32

5

16

2

4

4

43

168

1

84

2

28

3

4

7

44

176

1

88

2

44

2

4

11

45

184

1

92

2

4

23

4

1

46

192

1

96

2

48

2

4

12

47

192

1

96

2

24

4

4

6

48

192

1

64

3

16

4

4

4

49

192

1

24

8

8

3

4

2

50

208

1

104

2

52

2

4

13

51

216

1

108

2

36

3

4

9

52

224

1

112

2

56

2

4

14

53

240

1

120

2

60

2

4

15

54

240

1

80

3

20

4

4

5

55

240

1

48

5

16

3

8

2

56

240

1

24

10

12

2

4

3

57

256

1

128

2

64

2

4

16

58

256

1

128

2

32

4

4

8

59

256

1

16

16

8

2

4

2

60

264

1

132

2

44

3

4

11

61

272

1

136

2

68

2

4

17

62

272

1

68

4

4

17

4

1

63

272

1

16

17

8

2

4

2

 

Table 6.4.1.4.3-2: The offset \(\mathbf{k}_{\text{offset}}^{\mathbf{l}^{\mathbf{'}}}\) for SRS as a function of \(\mathbf{K}_{\text{TC}}\) and \(\mathbf{l}\mathbf{'}\).

\[\mathbf{K}_{\text{TC}}\]

\[\mathbf{k}_{\text{offset}}^{0},\ldots,\mathbf{k}_{\text{offset}}^{\mathbf{N}_{\text{symb}}^{\text{SRS}} - 1}\]

\[\mathbf{N}_{\text{symb}}^{\text{SRS}} = 1\]

\[\mathbf{N}_{\text{symb}}^{\text{SRS}} = 2\]

\[\mathbf{N}_{\text{symb}}^{\text{SRS}} = 4\]

\[\mathbf{N}_{\text{symb}}^{\text{SRS}} = 8\]

\[\mathbf{N}_{\text{symb}}^{\text{SRS}} = 12\]

2

0

0,1

0,1,0,1

-

-

4

-

0, 2

0, 2, 1, 3

0, 2, 1, 3, 0, 2, 1, 3

0, 2, 1, 3, 0, 2, 1, 3, 0, 2, 1, 3

8

-

-

0, 4, 2, 6

0, 4, 2, 6, 1, 5, 3, 7

0, 4, 2, 6, 1, 5, 3, 7, 0, 4, 2, 6

 

Table 6.4.1.4.3-3: The quantity \(\mathbf{k}_{\text{hop}}\) as a function of \({\bar{\mathbf{k}}}_{\text{hop}}\).

\[{\bar{\mathbf{k}}}_{\text{hop}}\]

\[\mathbf{k}_{\text{hop}}\]

 

\[\mathbf{P}_{\text{F}} = 1\]

\[\mathbf{P}_{\text{F}} = 2\]

\[\mathbf{P}_{\text{F}} = 4\]

0

0

0

0

1

-

1

2

2

-

-

1

3

-

-

3

 

6.4.1.4.4     Sounding reference signal slot configuration #

Throughout this clause, when the higher layer parameter numberOfHops is provided for SRS-PosResource, the sounding reference signal slot configuration applies to a given hop.

For an SRS resource configured as periodic or semi-persistent by the higher-layer parameter resourceType, a periodicity \(T_{\mathrm{SRS}}\) (in slots) and slot offset \(T_{\text{offset}}\) are configured according to the higher-layer parameter periodicityAndOffset-p or periodicityAndOffset-sp in the SRS-Resource IE, or periodicityAndOffset-p or periodicityAndOffset-sp in the SRS-PosResource IE. Candidate slots in which the configured SRS resource may be used for SRS transmission are the slots satisfying

\[\begin{matrix} {\left( {N_{\text{slot}}^{\text{frame},\mu}n_{\text{f}} + n_{\text{s,f}}^{\mu} - T_{\text{offset}}} \right)\text{mod}T_{\text{SRS}} = 0} \end{matrix}\]

and, if the higher-layer parameter srs-PosPeriodicConfigHyperSFN-Index is configured for a periodicity larger than or equal to \(2^{\mu} \bullet 10240\) slots, also

\[\begin{matrix} {\left( {n_{\text{HFN}} + N_{\text{SRS}}^{\text{HFN}}} \right)\text{mod}2 = 0} \end{matrix}\]

where \(N_{\text{SRS}}^{\text{HFN}} \in \left\{ 0,1 \right\}\) is given by the higher-layer parameter srs-PosPeriodicConfigHyperSFN-Index and \(n_{\text{HFN}}\) is the hyper-frame number.

SRS is transmitted as described in clause 6.2.1 of [6, TS 38.214].

7     Downlink #

7 .1    Overview #

7 .1.1    Overview of physical channels #

A downlink physical channel corresponds to a set of resource elements carrying information originating from higher layers. The following downlink physical channels are defined:

-    Physical Downlink Shared Channel, PDSCH

-    Physical Broadcast Channel, PBCH

-    Physical Downlink Control Channel, PDCCH.

7 .1.2    Overview of physical signals #

A downlink physical signal corresponds to a set of resource elements used by the physical layer but does not carry information originating from higher layers.

The following downlink physical signals are defined:

-    Demodulation reference signals, DM-RS

-    Phase-tracking reference signals, PT-RS

-    Positioning reference signal, PRS

-    Channel-state information reference signal, CSI-RS

-    Primary synchronization signal, PSS

-    Secondary synchronization signal, SSS

-    Wake-up signal, WUS

-    Low-power synchronization signal, LPSS

7 .2    Physical resources #

The frame structure and physical resources the UE shall assume when receiving downlink transmissions are defined in Clause 4.

The following antenna ports are defined for the downlink:

-    Antenna ports starting with 1000 for PDSCH

-    Antenna ports starting with 2000 for PDCCH

-    Antenna ports starting with 3000 for channel-state information reference signals

-    Antenna ports starting with 4000 for SS/PBCH block transmission

-    Antenna ports starting with 5000 for positioning reference signals

The UE shall not assume that two antenna ports are quasi co-located with respect to any QCL type unless specified otherwise.

For DM-RS associated with a PDSCH, the channel over which a PDSCH symbol on one antenna port is conveyed can be inferred from the channel over which a DM-RS symbol on the same antenna port is conveyed only if the two symbols are within the same resource as the scheduled PDSCH, in the same slot, and in the same PRG as described in clause 5.1.2.3 of [6, TS 38.214].

For DM-RS associated with a PDCCH, the channel over which a PDCCH symbol on one antenna port is conveyed can be inferred from the channel over which a DM-RS symbol on the same antenna port is conveyed only if the two symbols are within resources for which the UE may assume the same precoding being used as described in clause 7.3.2.2.

For DM-RS associated with a PBCH, the channel over which a PBCH symbol on one antenna port is conveyed can be inferred from the channel over which a DM-RS symbol on the same antenna port is conveyed only if the two symbols are within a SS/PBCH block transmitted within the same slot, and with the same block index according to clause 7.4.3.1.

7 .3    Physical channels #

7 .3.1.1    Scrambling #

Up to two codewords \(q \in \{0,1\}\) can be transmitted. In case of single-codeword transmission, \(q=0\).

For each codeword \(q\), the UE shall assume the block of bits \(b^{(q)}(0),\ldots,b^{(q)}\left( M_{\text{bit}}^{(q)} - 1 \right)\), where \(M_{\text{bit}}^{(q)}\) is the number of bits in codeword \(q\) transmitted on the physical channel, are scrambled prior to modulation, resulting in a block of scrambled bits \({\overset{\sim}{b}}^{(q)}(0),\ldots,{\overset{\sim}{b}}^{(q)}\left( M_{\text{bit}}^{(q)} - 1 \right)\)according to

    \({\overset{\sim}{b}}^{(q)}(i) = \left( {b^{(q)}(i) + c^{(q)}(i)} \right)\text{mod}2\)

where the scrambling sequence \(c^{(q)}(i)\) is given by clause 5.2.1. The scrambling sequence generator shall be initialized with

\[c_{\text{init}} = n_{\text{RNTI}} \cdot 2^{15} + q \cdot 2^{14} + n_{\text{ID}}\]

where

-    \(n_{\mathrm{ID}} \in \{0,1,\ldots,1023\}\) equals the higher-layer parameter dataScramblingIdentityPDSCH if configured and the RNTI equals the C-RNTI, MCS-C-RNTI, or CS-RNTI, and the transmission is not scheduled using DCI format 1_0 in a common search space;

-    \(n_{\text{ID}} \in \left\{ {0,1,\ldots,1023} \right\}\) equals the higher-layer parameter dataScramblingIdentityPDSCH in pdsch-ConfigMulticast if configured in a common MBS frequency resource for multicast and the RNTI equals the G-RNTI or the G-CS-RNTI;

-    \(n_{\text{ID}} \in \left\{ {0,1,\ldots,1023} \right\}\) equals the higher-layer parameter dataScramblingIdentityPDSCH in pdsch-ConfigMCCH or pdsch-ConfigMTCH if configured in a common MBS frequency resource for broadcast and the RNTI equals the MCCH-RNTI or G-RNTI, respectively;

-    \(n_{\text{ID}} \in \left\{ {0,1,\ldots,1023} \right\}\) equals

-    the higher-layer parameter dataScramblingIdentityPDSCH if the codeword is scheduled using a CORESET with CORESETPoolIndex equal to 0;

-    the higher-layer parameter dataScramblingIdentityPDSCH2 if the codeword is scheduled using a CORESET with CORESETPoolIndex equal to 1;

    if the higher-layer parameters dataScramblingIdentityPDSCH and dataScramblingIdentityPDSCH2 are configured together with the higher-layer parameter CORESETPoolIndex containing two different values, and the RNTI equals the C-RNTI, MCS-C-RNTI, or CS-RNTI, and the transmission is not scheduled using DCI format 1_0 in a common search space;

-    \(n_{\text{ID}} = N_{\text{ID}}^{\text{cell}}\) otherwise

and where \(n_{\mathrm{RNTI}}\) corresponds to the RNTI associated with the PDSCH transmission as described in clause 5.1 of [6, TS 38.214].

7 .3.1.2    Modulation #

For each codeword \(q\), the UE shall assume the block of scrambled bits \({\overset{\sim}{b}}^{(q)}(0),\ldots,{\overset{\sim}{b}}^{(q)}\left( M_{\text{bit}}^{(q)} - 1 \right)\) are modulated as described in clause 5.1 using one of the modulation schemes in Table 7.3.1.2-1, resulting in a block of complex-valued modulation symbols \(d^{(q)}(0),\ldots,d^{(q)}\left( M_{\text{symb}}^{(q)} - 1 \right)\).

Table 7.3.1.2-1: Supported modulation schemes.

Modulation scheme

Modulation order \(\mathcal{Q}_m\)

QPSK

2

16QAM

4

64QAM

6

256QAM

8

1024QAM

10

 

7 .3.1.3    Layer mapping #

The UE shall assume that complex-valued modulation symbols for each of the codewords to be transmitted are mapped onto one or several layers according to Table 7.3.1.3-1. Complex-valued modulation symbols \(d^{(q)}(0),\ldots,d^{(q)}\left( M_{\text{symb}}^{(q)} - 1 \right)\) for codeword \(q\) shall be mapped onto the layers \(x(i) = \begin{bmatrix} {x^{(0)}(i)} & \ldots & {x^{({\upsilon - 1})}(i)} \end{bmatrix}^{\text{T}}\), \(i = 0,1,\ldots,M_{\text{symb}}^{\text{layer}} - 1\) where \(\upsilon\) is the number of layers and \(M_{\text{symb}}^{\text{layer}}\) is the number of modulation symbols per layer.

Table 7.3.1.3-1: Codeword-to-layer mapping for spatial multiplexing.

Number of layers

Number of codewords

Codeword-to-layer mapping

\(i = 0, 1, \ldots, M_{\mathrm{symb}}^{\mathrm{layer}} - 1\)

1

1

\(\[x^{(0)}(i)=d^{(0)}(i)\]\)

\(M_{\mathrm{symb}}^{\mathrm{layer}} = M_{\mathrm{symb}}^{(0)}\)

2

1

\(\begin{aligned} x^{(0)}(i) &= d^{(0)}(2i) \\ x^{(1)}(i) &= d^{(0)}(2i+1) \end{aligned}\)

\(M^{\text{layer}}_{\text{symb}}=M^{(0)}_{\text{symb}}/2\)

3

1

\(\[ \begin{aligned} x^{(0)}(i) &= d^{(0)}(3i),\\ x^{(1)}(i) &= d^{(0)}(3i+1),\\ x^{(2)}(i) &= d^{(0)}(3i+2). \end{aligned} \]\)

\(M_{\text{symb}}^{\text{layer}} = M_{\text{symb}}^{(0)}/3\)

4

1

\(\begin{aligned} x^{(0)}(i) &= d^{(0)}(4i)\\ x^{(1)}(i) &= d^{(0)}(4i+1)\\ x^{(2)}(i) &= d^{(0)}(4i+2)\\ x^{(3)}(i) &= d^{(0)}(4i+3) \end{aligned}\)

\(M_{\text{symb}}^{\text{layer}} = M_{\text{symb}}^{(0)} / 4\)

5

2

\(\begin{aligned} x^{(0)}(i) &= d^{(0)}(2i) \\ x^{(1)}(i) &= d^{(0)}(2i+1) \end{aligned}\)

\(M^{\text{layer}}_{\text{symb}} = M^{(0)}_{\text{symb}}/2 = M^{(1)}_{\text{symb}}/3\)

\(\begin{aligned} x^{(2)}(i) &= d^{(1)}(3i)\\ x^{(3)}(i) &= d^{(1)}(3i+1)\\ x^{(4)}(i) &= d^{(1)}(3i+2) \end{aligned}\)

6

2

\(\[ \begin{aligned} x^{(0)}(i) &= d^{(0)}(3i),\\ x^{(1)}(i) &= d^{(0)}(3i+1),\\ x^{(2)}(i) &= d^{(0)}(3i+2). \end{aligned} \]\)

\(M_{\text{symb}}^{\text{layer}} = M_{\text{symb}}^{(0)}/3 = M_{\text{symb}}^{(1)}/3\)

\(\begin{aligned} x^{(3)}(i) &= d^{(1)}(3i) \\ x^{(4)}(i) &= d^{(1)}(3i+1) \\ x^{(5)}(i) &= d^{(1)}(3i+2) \end{aligned}\)

7

2

\(\[ \begin{aligned} x^{(0)}(i) &= d^{(0)}(3i),\\ x^{(1)}(i) &= d^{(0)}(3i+1),\\ x^{(2)}(i) &= d^{(0)}(3i+2). \end{aligned} \]\)

\(M^{\mathrm{layer}}_{\mathrm{symb}} = M^{(0)}_{\mathrm{symb}}/3 = M^{(1)}_{\mathrm{symb}}/4\)

\(\begin{aligned} x^{(3)}(i) &= d^{(1)}(4i) \\ x^{(4)}(i) &= d^{(1)}(4i+1) \\ x^{(5)}(i) &= d^{(1)}(4i+2) \\ x^{(6)}(i) &= d^{(1)}(4i+3) \end{aligned}\)

8

2

\(\begin{aligned} x^{(0)}(i) &= d^{(0)}(4i)\\ x^{(1)}(i) &= d^{(0)}(4i+1)\\ x^{(2)}(i) &= d^{(0)}(4i+2)\\ x^{(3)}(i) &= d^{(0)}(4i+3) \end{aligned}\)

\(M_{\text{symb}}^{\text{layer}} = M_{\text{symb}}^{(0)}/4 = M_{\text{symb}}^{(1)}/4\)

\(\begin{aligned} x^{(4)}(i) &= d^{(1)}(4i) \\ x^{(5)}(i) &= d^{(1)}(4i+1) \\ x^{(6)}(i) &= d^{(1)}(4i+2) \\ x^{(7)}(i) &= d^{(1)}(4i+3) \end{aligned}\)

 

7 .3.1.4    Antenna port mapping #

The block of vectors \(\begin{bmatrix} {x^{(0)}(i)} & \ldots & {x^{({\upsilon - 1})}(i)} \end{bmatrix}^{\text{T}}\), \(i = 0,1,\ldots,M_{\text{symb}}^{\text{layer}} - 1\) shall be mapped to antenna ports according to

 

\(\begin{bmatrix} y^{(p_0)}(i)\\ \vdots\\ y^{(p_{v-1})}(i) \end{bmatrix} = \begin{bmatrix} x^{(0)}(i)\\ \vdots\\ x^{(v-1)}(i) \end{bmatrix}\)

where \(i = 0,1,\ldots,M_{\text{symb}}^{\text{ap}} - 1\), \(M_{\text{symb}}^{\text{ap}} = M_{\text{symb}}^{\text{layer}}\). The set of antenna ports \(\{p_{0},\ldots,P_{\nu-1}\}\) shall be determined according to the procedure in [4, TS 38.212].

7 .3.1.5    Mapping to virtual resource blocks #

The UE shall, for each of the antenna ports used for transmission of the physical channel, assume the block of complex-valued symbols \(y^{(p)}(0),\ldots,y^{(p)}\left( M_{\text{symb}}^{\text{ap}} - 1 \right)\) conform to the downlink power allocation specified in [6, TS 38.214] and are mapped in sequence starting with \(y^{(p)}(0)\) to resource elements \(\left( {k^{'},l} \right)_{p,\mu}\) in the virtual resource blocks assigned for transmission which meet all of the following criteria:

-    they are in the virtual resource blocks assigned for transmission;

-    the corresponding physical resource blocks are declared as available for PDSCH according to clause 5.1.4 of [6, TS 38.214];

-    the corresponding resource elements in the corresponding physical resource blocks are

-    not used for transmission of the associated DM-RS or DM-RS intended for other co-scheduled UEs as described in clause 7.4.1.1.2;

-    not used for non-zero-power CSI-RS, which is according to clause 7.4.1.5 and not configured by the TRS-ResourceSet IE, if the corresponding physical resource blocks are for a PDSCH scheduled by a PDCCH with the CRC scrambled by C-RNTI, MCS-C-RNTI, CS-RNTI, G-RNTI for multicast, G-CS-RNTI, or a PDSCH with SPS, except if the non-zero-power CSI-RS is a CSI-RS configured by the higher-layer parameter CSI-RS-Resource-Mobility in the MeasObjectNR IE or except if the non-zero-power CSI-RS is an aperiodic non-zero-power CSI-RS resource;

-    not used for PT-RS according to clause 7.4.1.2;

-    not declared as 'not available for PDSCH according to clause 5.1.4 of [6, TS 38.214].

The mapping to resource elements \((k',l)_{p,\mu}\) allocated for PDSCH according to [6, TS 38.214] and not reserved for other purposes shall be in increasing order of first the index \(k'\) over the assigned virtual resource blocks, where \(k^{'} = 0\) is the first subcarrier in the lowest-numbered virtual resource block assigned for transmission, and then the index \(l\).

7.3.1.6     Mapping from virtual to physical resource blocks #

The UE shall assume the virtual resource blocks are mapped to physical resource blocks according to the indicated mapping scheme, non-interleaved or interleaved mapping. If no mapping scheme is indicated, the UE shall assume non-interleaved mapping.

For non-interleaved VRB-to-PRB mapping, virtual resource block \(n\) is mapped to physical resource block \(n\), except for PDSCH transmissions scheduled with DCI format 1_0 in a common search space in which case virtual resource block \(n\) is mapped to physical resource block \(n + N_{\text{start}}^{\text{CORESET}}\) where \(N_{\text{start}}^{\text{CORESET}}\) is the lowest-numbered physical resource block in the control resource set where the corresponding DCI was received. When two PDCCH candidates from two linked common search space sets as indicated by the higher-layer parameter searchSpaceLinking are detected, and the two linked common search space sets are associated with different control resource sets, the control resource set with the lowest number among the two linked control resource sets is used to determine \(N_{\text{start}}^{\text{CORESET}}\).

For interleaved VRB-to-PRB mapping, the mapping process is defined by:

-    Resource block bundles are defined as

-    for PDSCH transmissions scheduled with DCI format 1_0 with the CRC scrambled by SI-RNTI in Type0-PDCCH common search space in CORESET 0, the set of \(N_{\text{BWP,init}}^{\text{size}}\) resource blocks in CORESET 0 are divided into \(N_{\text{bundle}} = \left\lceil {N_{\text{BWP,init}}^{\text{size}}/L} \right\rceil\) resource-block bundles in increasing order of the resource-block number and bundle number where \(L = 2\) is the bundle size and \(N_{\text{BWP,init}}^{\text{size}}\) is the size of CORESET 0.

-    resource block bundle \(N_{\text{bundle}} - 1\) consists of \(N_{\text{BWP,init}}^{\text{size}}\text{mod}L\) resource blocks if \(N_{\text{BWP,init}}^{\text{size}}\text{mod}L > 0\) and \(L\) resource blocks otherwise,

-    all other resource block bundles consists of \(L\) resource blocks.

-    for PDSCH transmissions scheduled with DCI format 1_0 in any common search space in bandwidth part \(i\) with starting position \(N_{\text{BWP,}i}^{\text{start}}\), other than Type0-PDCCH common search space in CORESET 0, the set of \(N_{\text{BWP,init}}^{\text{size}}\) virtual resource blocks \(\left\{ {0,1,\ldots,N_{\text{BWP,init}}^{\text{size}} - 1} \right\}\), where \(N_{\text{BWP,init}}^{\text{size}}\) is the size of CORESET 0 if CORESET 0 is configured for the cell and the size of initial downlink bandwidth part if CORESET 0 is not configured for the cell, are divided into \(N_{\text{bundle}}\) virtual resource-block bundles in increasing order of the virtual resource-block number and virtual bundle number and the set of \(N_{\text{BWP,init}}^{\text{size}}\) physical resource blocks \(\left\{ {N_{\text{start}}^{\text{CORESET}},N_{\text{start}}^{\text{CORESET}} + 1,\ldots,N_{\text{start}}^{\text{CORESET}} + N_{\text{BWP,init}}^{\text{size}} - 1} \right\}\) are divided into \(N_{\text{bundle}}\) physical resource-block bundles in increasing order of the physical resource-block number and physical bundle number, where \(N_{\text{bundle}} = \left\lceil {\left( {N_{\text{BWP,init}}^{\text{size}} + \left( {N_{\text{BWP,}i}^{\text{start}} + N}_{\text{start}}^{\text{CORESET}} \right)\text{mod}L} \right)/L} \right\rceil\), \(L = 2\) is the bundle size, and \(N_{\text{start}}^{\text{CORESET}}\) is the lowest-numbered physical resource block in the control resource set where the corresponding DCI was received. When two PDCCH candidates from two linked search space sets as indicated by the higher-layer parameter searchSpaceLinking are detected, and the two linked search space sets are associated with different control resource sets, the control resource set with the lowest number among the two linked control resource sets is used to determine \(N_{\text{start}}^{\text{CORESET}}\).

-    resource block bundle 0 consists of \(L - \left( {\left( {N_{\text{BWP,}i}^{\text{start}} + N}_{\text{start}}^{\text{CORESET}} \right)\text{mod}L} \right)\) resource blocks,

-    resource block bundle \(N_{\text{bundle}} - 1\) consists of \(\left( {{N_{\text{BWP,init}}^{\text{size}} + N}_{\text{BWP,}i}^{\text{start}} + N}_{\text{start}}^{\text{CORESET}} \right)\text{mod}L\) resource blocks if \(\left( {{N_{\text{BWP,init}}^{\text{size}} + N}_{\text{BWP,}i}^{\text{start}} + N}_{\text{start}}^{\text{CORESET}} \right)\text{mod}L > 0\) and \(L\) resource blocks otherwise,

-    all other resource block bundles consists of \(L\) resource blocks.

-    for all other PDSCH transmissions, the set of \(N_{\text{BWP},i}^{\text{size}}\) resource blocks in bandwidth part \(i\) with starting position \(N_{\text{BWP,}i}^{\text{start}}\) are divided into \(N_{\text{bundle}} = \left\lceil {\left( {N_{\text{BWP},i}^{\text{size}} + \left( {N_{\text{BWP},i}^{\text{start}}\text{mod}L_{i}} \right)} \right)/L_{i}} \right\rceil\) resource-block bundles in increasing order of the resource-block number and bundle number where \(L_i\) is the bundle size for bandwidth part \(i\) provided by the higher-layer parameter vrb-ToPRB-Interleaver for DCI formats 1_0, 1_1, and 1_3 in a UE-specific search space, or vrb-ToPRB-InterleaverDCI-1-2 for DCI format 1_2, and

-    resource block bundle 0 consists of \(L_i - \left(N^{\text{start}}_{\mathrm{BWP},i} \bmod L_i\right)\) resource blocks,

-    resource block bundle \(N_{\text{bundle}}-1\) consists of \(\left(N_{\mathrm{BWP},i}^{\mathrm{start}} + N_{\mathrm{BWP},i}^{\mathrm{size}}\right)\bmod L_i\) resource blocks if \(\left(N_{BWP,i}^{\text{start}} + N_{BWP,i}^{\text{size}}\right) \bmod L_i > 0\) and \(L_i\) resource blocks otherwise,

-    all other resource block bundles consists of \(L_i\) resource blocks.

-    Virtual resource blocks in the interval \(j \in \{0,1,\ldots,N_{\text{bundle}}-1\}\) are mapped to physical resource blocks according to

-    virtual resource block bundle \(N_{\text{bundle}}-1\) is mapped to physical resource block bundle \(N_{\text{bundle}}-1\)

-    virtual resource block bundle \(j \in \{0,1,\ldots,N_{\text{bundle}}-2\}\) is mapped to physical resource block bundle \(f(j)\) where

\(\begin{aligned} f(j) &= rC + c \\ j &= cR + r \\ r &= 0,1,\ldots,R-1 \\ c &= 0,1,\ldots,C-1 \\ R &= 2 \\ C &= \left\lceil \frac{N_{\text{bundle}}}{R} \right\rceil \end{aligned}\)

-    The UE is not expected to be configured with \(L_{i} = 2\) simultaneously with a PRG size of 4 as defined in [6, TS 38.214]

The UE may assume that the same precoding in the frequency domain is used within a PRB bundle and the bundle size is determined by clause 5.1.2.3 in [6, TS 38.214]. The UE shall not make any assumption that the same precoding is used for different bundles of common resource blocks.

For PDSCH transmissions scheduled by DCI format 4_1 or 4_2, and using G-RNTI or G-CS-RNTI, the quantities \(N_{\text{BWP,}i}^{\text{start}}\) and \(N_{\text{BWP},i}^{\text{size}}\) in this clause are replaced by \(N_{\text{MBS,}i}^{\text{start}}\) and \(N_{\text{MBS},i}^{\text{size}}\), respectively, and \(L_{i}\) is the bundle size for the common MBS frequency resource provided by the higher-layer parameter vrb-ToPRB-Interleaver in pdsch-ConfigMulticast.

For PDSCH transmissions scheduled by DCI format 4_0, and using G-RNTI for broadcast, MCCH-RNTI, or Multicast-MCCH-RNTI, the quantities \(N_{\text{BWP,}i}^{\text{start}}\) and \(N_{\text{BWP},i}^{\text{size}}\) in this clause are replaced by \(N_{\text{MBS,}i}^{\text{start}}\) and \(N_{\text{MBS},i}^{\text{size}}\), respectively, and \(L_{i} = 2\).

7.3.2.1     Control-channel element (CCE) #

A physical downlink control channel consists of one or more control-channel elements (CCEs) as indicated in Table 7.3.2.1-1.

Table 7.3.2.1-1: Supported PDCCH aggregation levels.

Aggregation level

Number of CCEs

1

1

2

2

4

4

8

8

16

16

 

7.3.2.2     Control-resource set (CORESET) #

A control-resource set consists of \(N_{\text{RB}}^{\text{CORESET}}\) resource blocks in the frequency domain and \(N_{\text{symb}}^{\text{CORESET}} \in \left\{ {1,2,3} \right\}\) symbols in the time domain.

A control-channel element consists of 6 resource-element groups (REGs) where a resource-element group equals one resource block during one OFDM symbol. Resource-element groups within a control-resource set are numbered in increasing order in a time-first manner, starting with 0 for the first OFDM symbol and the lowest-numbered resource block in the control resource set.

A UE can be configured with multiple="multiple" control-resource sets. Each control-resource set is associated with one CCE-to-REG mapping only.

The CCE-to-REG mapping for a control-resource set can be interleaved or non-interleaved and is described by REG bundles:

-    REG bundle \(i\) is defined as REGs \(\left\{ {iL,iL + 1,\ldots,iL + L - 1} \right\}\) where \(L\) is the REG bundle size, \(i = 0,1,\ldots,{N_{\text{REG}}^{\text{CORESET}}/L} - 1\), and \(N_{\text{REG}}^{\text{CORESET}} = N_{\text{RB}}^{\text{CORESET}}N_{\text{symb}}^{\text{CORESET}}\) is the number of REGs in the CORESET

-    CCE \(j\) consists of REG bundles \(\left\{ {f\left( {{6j}/L} \right),f\left( {{{6j}/L} + 1} \right),\ldots,f\left( {{6j}/L} + {6/L} - 1 \right)} \right\}\) where \(f( \bullet )\) is an interleaver

For non-interleaved CCE-to-REG mapping, \(L = 6\) and \(f(x) = x\).

For interleaved CCE-to-REG mapping, \(L \in \left\{ 2,6 \right\}\) for \(N_{\text{symb}}^{\text{CORESET}} = 1\) and \(L \in \left\{ {N_{\text{symb}}^{\text{CORESET}},6} \right\}\) for \(N_{\text{symb}}^{\text{CORESET}} \in \left\{ 2,3 \right\}\). The interleaver is defined by

\[\begin{matrix} {f(x) = \left( {rC + c + n_{\text{shift}}} \right)\text{mod}\left( {N_{\text{REG}}^{\text{CORESET}}/L} \right)} \\ {x = cR + r} \\ {r = 0,1,\ldots,R - 1} \\ {c = 0,1,\ldots,C - 1} \\ {C = {N_{\text{REG}}^{\text{CORESET}}/(LR)}} \end{matrix}\]

where \(R \in \left\{ {2,3,6} \right\}\).

The UE is not expected to handle configurations resulting in the quantity \(C\) not being an integer.

For a CORESET configured by the ControlResourceSet IE:

-    \(N_{\text{RB}}^{\text{CORESET}}\) is given by the higher-layer parameter frequencyDomainResources;

-    \(N_{\text{symb}}^{\text{CORESET}}\) is given by the higher-layer parameter duration, where \(N_{\text{symb}}^{\text{CORESET}} = 3\) is supported only if the higher-layer parameter dmrs-TypeA-Position equals 'pos3';

-    interleaved or non-interleaved mapping is given by the higher-layer parameter cce-REG-MappingType;

-    \(L\) equals 6 for non-interleaved mapping and is given by the higher-layer parameter reg-BundleSize for interleaved mapping;

-    \(R\) is given by the higher-layer parameter interleaverSize;

-    \(n_{\text{shift}} \in \left\{ {0,1,\ldots,274} \right\}\) is given by the higher-layer parameter shiftIndex if provided, otherwise \(n_{\text{shift}} = N_{\text{ID}}^{\text{cell}}\);

-    for both interleaved and non-interleaved mapping:

-    if the higher-layer parameter precoderGranularity equals sameAsREG-bundle the UE may assume the same precoding being used within a REG bundle

-    if the higher-layer parameter precoderGranularity equals allContiguousRBs,

-    the UE may assume the same precoding being used across the all resource-element groups within the set of contiguous resource blocks in the CORESET;

-    the UE may assume that no resource elements in the CORESET overlap with an SSB;

-    if the UE is not provided with the higher-layer parameter pdcch-CandidateReceptionWith-CRS-Overlap, the UE may assume that no resource elements in the CORESET overlap with LTE cell-specific reference signals as indicated by the higher-layer parameter lte-CRS-ToMatchAround, lte-CRS-PatternList1, lte-CRS-PatternList2, lte-CRS-PatternList3, or lte-CRS-PatternList4.

For CORESET 0 configured by the ControlResourceSetZero IE:

-    \(N_{\text{RB}}^{\text{CORESET}}\) and \(N_{\text{symb}}^{\text{CORESET}}\) are defined by clause 13 of [5, TS 38.213];

-    the UE may assume interleaved mapping;

-    \(L = 6\);

-    \(R = 2\);

-    \(n_{\text{shift}} = N_{\text{ID}}^{\text{cell}}\);

-    the UE may assume normal cyclic prefix when CORESET 0 is configured by MIB or SIB1;

-    the UE may assume the same precoding being used within a REG bundle.

For CORESET 0 on a carrier where the SS/PBCH block is detected at sync raster points defined in Tables 5.4.3.1-2 or 5.4.3.1-3 of [14, TS 38.101-1] and configured by the ControlResourceSetZero IE:

-    \(N_{\text{RB}}^{\text{CORESET}}\) and \(N_{\text{symb}}^{\text{CORESET}}\) are defined by Table 13-0 in clause 13 of [5, TS 38.213];

-    if \(N_{\text{RB}}^{\text{CORESET}} = 12\) on a carrier with a channel bandwidth of 3 MHz, the CORESET is obtained by applying the description above assuming interleaved mapping with \(R = 2\);

-    if \(N_{\text{RB}}^{\text{CORESET}} = 24\) on a carrier with a channel bandwidth of 3 MHz, the CORESET is obtained by applying the description above assuming interleaved mapping with \(R = 2\) or non-interleaved mapping as defined by clause 13 of [5, TS 38.213], followed by puncturing the 9 highest-numbered resource blocks to obtain the 15 resource blocks forming CORESET 0;

-    if \(N_{\text{RB}}^{\text{CORESET}} = 24\) on a carrier with a channel bandwidth of 5 MHz, the CORESET is obtained by applying the description above assuming interleaved mapping with \(R = 2\), followed by puncturing the 4 highest-numbered resource blocks to obtain the 20 resource blocks forming CORESET 0;

-    \(L = 6\);

-    \(n_{\text{shift}} = N_{\text{ID}}^{\text{cell}}\);

-    the UE may assume normal cyclic prefix when CORESET 0 is configured by MIB or SIB1;

-    the UE may assume the same precoding being used within a REG bundle.

7.3.2.3     Scrambling #

The UE shall assume the block of bits \(b(0),\ldots,b\left( M_{\text{bit}}^{} - 1 \right)\), where \(M_{\text{bit}}^{}\) is the number of bits transmitted on the physical channel, is scrambled prior to modulation, resulting in a block of scrambled bits \(\overset{\sim}{b}(0),\ldots,\overset{\sim}{b}\left( M_{\text{bit}}^{} - 1 \right)\) according to

\[\overset{\sim}{b}(i) = \left( {b(i) + c(i)} \right)\text{mod}2\]

where the scrambling sequence \(c(i)\) is given by clause 5.2.1. The scrambling sequence generator shall be initialized with

    \(c_{\mathrm{init}}=\left(n_{\mathrm{RNTI}}\cdot 2^{16}+n_{\mathrm{ID}}\right)\bmod 2^{31}\)

where

-    for a UE-specific search space as defined in clause 10 of [5, TS 38.213], \(n_{\mathrm{ID}} \in \{0,1,\ldots,65535\}\) equals the higher-layer parameter pdcch-DMRS-ScramblingID if configured;

-    for a PDCCH with the CRC scrambled by G-RNTI, G-CS-RNTI, MCCH-RNTI, or Multicast-MCCH-RNTI in a common search space as defined in clause 10 of [5, TS 38.213], \(n_{\text{ID}} \in \left\{ {0,1,\ldots,65535} \right\}\) equals the higher-layer parameter pdcch-DMRS-ScramblingID if configured in a common MBS frequency resource;

-    \(n_{\text{ID}} = N_{\text{ID}}^{\text{cell}}\) otherwise

and where

-    \(n_{\mathrm{RNTI}}\) is given by the C-RNTI for a PDCCH in a UE-specific search space if the higher-layer parameter pdcch-DMRS-ScramblingID is configured, and

-    \(n_{\mathrm{RNTI}}=0\) otherwise.

7.3.2.4     PDCCH modulation #

The UE shall assume the block of bits \(\overset{\sim}{b}(0),\ldots,\overset{\sim}{b}\left( {M_{\text{bit}} - 1} \right)\) to be QPSK modulated as described in clause 5.1.3, resulting in a block of complex-valued modulation symbols \(d(0),\ldots,d\left( M_{\text{symb}} - 1 \right)\).

7.3.2.5     Mapping to physical resources #

The UE shall assume the block of complex-valued symbols \(d(0),\ldots,d\left( M_{\text{symb}} - 1 \right)\) to be scaled by a factor \(\beta_{\mathrm{PDCCH}}\) and mapped to resource elements \(\left( {k,l} \right)_{p,\mu}\) used for the monitored PDCCH and not used for the associated PDCCH DMRS in increasing order of first \(k\), then \(l\). The antenna port \(p=2000\).

7 .3.3    Physical broadcast channel #

7.3.3.1     Scrambling #

The UE shall assume the block of bits\(b(0),\ldots,b\left( M_{\text{bit}}^{} - 1 \right)\), where \(M_{\mathrm{bit}}\) is the number of bits transmitted on the physical broadcast channel, are scrambled prior to modulation, resulting in a block of scrambled bits \(\overset{\sim}{b}(0),\ldots,\overset{\sim}{b}\left( M_{\text{bit}}^{} - 1 \right)\) according to

\[\overset{\sim}{b}(i) = \left( {b(i) + c\left( i + vM_{\text{bit}} \right)} \right)\text{mod}2\]

where the scrambling sequence \(c(i)\) is given by clause 5.2. The scrambling sequence shall be initialized with \(c_{\text{init}} = N_{\text{ID}}^{\text{cell}}\) at the start of each SS/PBCH block where

-    for \({\bar{L}}_{\max} = 4\), \(v\) is the two least significant bits of the candidate SS/PBCH block index

-    for \({\bar{L}}_{\max} > 4\), \(v\) is the three least significant bits of the candidate SS/PBCH block index

with \({\bar{L}}_{\max}\) being the maximum number of candidate SS/PBCH blocks in a half frame, as described in [5, TS 38.213].

7.3.3. 2    Modulation #

The UE shall assume the block of bits \(\overset{\sim}{b}(0),\ldots,\overset{\sim}{b}\left( M_{\text{bit}}^{} - 1 \right)\) are QPSK modulated as described in clause 5.1.3, resulting in a block of complex-valued modulation symbols \(d_{\text{PBCH}}(0),\ldots,d_{\text{PBCH}}\left( M_{\text{symb}} - 1 \right)\).

7.3.3. 3    Mapping to physical resources #

Mapping to physical resources is described in clause 7.4.3.

7 .4    Physical signals #

7 .4.1    Reference signals #

7 .4.1.1    Demodulation reference signals for PDSCH #

7.4.1.1.1     Sequence generation #

The UE shall assume the sequence \(r(n)\) is defined by

\(r(n)=\frac{1}{\sqrt{2}}\left(1-2\cdot c(2n)\right)+j\frac{1}{\sqrt{2}}\left(1-2\cdot c(2n+1)\right)\).

where the pseudo-random sequence \(c(i)\) is defined in clause 5.2.1. The pseudo-random sequence generator shall be initialized with

\[c_{\text{init}} = \left( {2^{17}\left( {N_{\text{symb}}^{\text{slot}}n_{\text{s,f}}^{\mu} + l + 1} \right)\left( {2N_{\text{ID}}^{{\bar{n}}_{\text{SCID}}^{\bar{\lambda}}} + 1} \right) + 2^{17}\left\lfloor \frac{\bar{\lambda}}{2} \right\rfloor + 2N_{\text{ID}}^{{\bar{n}}_{\text{SCID}}^{\bar{\lambda}}} + {\bar{n}}_{\text{SCID}}^{\bar{\lambda}}} \right)\text{mod}2^{31}\]

where \(l\) is the OFDM symbol number within the slot, \(n_{\text{s,f}}^{\mu}\) is the slot number within a frame, and

-    \(N_{\text{ID}}^{0},N_{\text{ID}}^{1} \in \left\{ {0,1,\ldots,65535} \right\}\) are given by the higher-layer parameters scramblingID0 and scramblingID1, respectively, in the DMRS-DownlinkConfig IE if provided and the PDSCH is scheduled by PDCCH using DCI format 1_1, 1_2, or 1_3 with the CRC scrambled by C-RNTI, MCS-C-RNTI, or CS-RNTI;

-    \(N_{\text{ID}}^{0} \in \left\{ {0,1,\ldots,65535} \right\}\) is given by the higher-layer parameter scramblingID0 in the DMRS-DownlinkConfig IE if provided and the PDSCH is scheduled by PDCCH using DCI format 1_0 with the CRC scrambled by C-RNTI, MCS-C-RNTI, or CS-RNTI;

-    \(N_{\text{ID}}^{0},N_{\text{ID}}^{1} \in \left\{ {0,1,\ldots,65535} \right\}\) are given by the higher-layer parameters scramblingID0 and scramblingID1, respectively, in the DMRS-DownlinkConfig IE in pdsch-ConfigMulticast if provided in a common MBS frequency resource for multicast and the PDSCH is scheduled by PDCCH using DCI format 4_2 with the CRC scrambled by G-RNTI or G-CS-RNTI;

-    \(N_{\text{ID}}^{0} \in \left\{ {0,1,\ldots,65535} \right\}\) is given by the higher-layer parameter scramblingID0 in the DMRS-DownlinkConfig IE in pdsch-ConfigMulticast if provided in a common MBS frequency resource for multicast and the PDSCH is scheduled by PDCCH using DCI format 4_1 with the CRC scrambled by G-RNTI or G-CS-RNTI;

-    \(N_{\text{ID}}^{0} \in \left\{ {0,1,\ldots,65535} \right\}\) is given by the higher-layer parameter scramblingID0 in pdsch-ConfigMCCH or pdsch-ConfigMTCH if provided in a common MBS frequency resource for broadcast and the PDSCH is scheduled by PDCCH with the CRC scrambled by MCCH-RNTI or G-RNTI, respectively;

-    \(N_{\text{ID}}^{{\bar{n}}_{\text{SCID}}^{\bar{\lambda}}} = N_{\text{ID}}^{\text{cell}}\) otherwise;

-    \({\bar{n}}_{\text{SCID}}^{\bar{\lambda}}\text{and}\bar{\lambda}\text{are}\) given by

-    if the higher-layer parameter dmrs-Downlink in the DMRS-DownlinkConfig IE is provided

\[{\bar{n}}_{\text{SCID}}^{\bar{\lambda}} = \left\{ \begin{matrix} n_{\text{SCID}} & {\lambda = 0\text{or}\lambda = 2} \\ {1 - n_{\text{SCID}}} & {\lambda = 1} \end{matrix} \right.\]

\[\begin{matrix} {\bar{\lambda} = \lambda} \end{matrix}\]

    where λ is the CDM group defined in clause 7.4.1.1.2.

-    otherwise by

\[\begin{matrix} {{\bar{n}}_{\text{SCID}}^{\bar{\lambda}} = n_{\text{SCID}}} \end{matrix}\]

\[\begin{matrix} {\bar{\lambda} = 0} \end{matrix}\]

The quantity \(n_{\text{SCID}} \in \left\{ {0,1} \right\}\) is given by the DM-RS sequence initialization field, if present, in the DCI associated with the PDSCH transmission if DCI format 1_1, 1_2, 1_3, or 4_2 in [4, TS 38.212] is used, otherwise \(n_{\text{SCID}} = 0\).

7.4.1.1.2     Mapping to physical resources #

The UE shall assume the PDSCH DM-RS being mapped to physical resources according to configuration type 1 or configuration type 2 as given by the higher-layer parameter dmrs-Type.

The UE shall assume the sequence \(r(m)\) is scaled by a factor \(\beta_{\text{PDSCH}}^{\text{DMRS}}\) to conform with the transmission power specified in [6, TS 38.214] and mapped to resource elements \(\left( {k,l} \right)_{p,\mu}\) according to

-    if the higher-layer parameter dmrs-TypeEnh is configured and the PDSCH is not scheduled by DCI format 1_0, 4_0, or 4_1

ak,lpj,μ=βPDSCHDMRSwfk'wtl'r4n+k'k=8n+2k'+Δconfiguration type 112n+k'+Δconfiguration type 2, k'=0,112n+k'+Δ+4configuration type 2, k'=2,3k'=0,1,2,3l=l+l'n=0,1,j=0,1,,υ-1

-    otherwise

ak,lpj,μ=βPDSCHDMRSwfk'wtl'r2n+k'k=4n+2k'+Δconfiguration type 16n+k'+Δconfiguration type 2k'=0,1l=l+l'n=0,1,j=0,1,,υ-1

where \(w_f(k')\), \(w_t(l')\), and \(\Delta\) are given by Tables 7.4.1.1.2-1 and 7.4.1.1.2-2 and the following conditions are fulfilled:

-    the resource elements are within the common resource blocks allocated for PDSCH transmission

The reference point for \(k\) is

-    subcarrier 0 of the lowest-numbered resource block in CORESET 0 if the corresponding PDCCH is associated with CORESET 0 and Type0-PDCCH common search space and is addressed to SI-RNTI;

-    otherwise, subcarrier 0 in common resource block 0

The reference point for \(l\) and the position \(\ell_0\) of the first DM-RS symbol depends on the mapping type:

-    for PDSCH mapping type A:

-    \(l\) is defined relative to the start of the slot

-    \(l_{0}=3\)if the higher-layer parameter dmrs-TypeA-Position is equal to 'pos3' and \(l_{0}=2\) otherwise

-    for PDSCH mapping type B:

-    \(l\) is defined relative to the start of the scheduled PDSCH resources

-    \(l_{0} = 0\)

The position(s) of the DM-RS symbols is given by \(\overline{l}\) and duration \(l_{\text{d}}\) where

-    for PDSCH mapping type A, \(l_{\text{d}}\) is the duration between the first OFDM symbol of the slot and the last OFDM symbol of the scheduled PDSCH resources in the slot

-    for PDSCH mapping type B, \(l_{\text{d}}\) is the duration of the scheduled PDSCH resources

and according to Tables 7.4.1.1.2-3 and 7.4.1.1.2-4.

For PDSCH mapping type A

-    the case dmrs-AdditionalPosition equals to 'pos3' is only supported when dmrs-TypeA-Position is equal to 'pos2';

-    \(l_{\text{d}} = 3\) and \(l_{\text{d}} = 4\) symbols in Tables 7.4.1.1.2-3 and 7.4.1.1.2-4 respectively is only applicable when dmrs-TypeA-Position is equal to 'pos2';

-    single-symbol DM-RS, \(l_{1} = 11\) except if all of the following conditions are fulfilled in which case \(l_{1} = 12\):

-    the higher-layer parameter lte-CRS-ToMatchAround, lte-CRS-PatternList1, lte-CRS-PatternList2, lte-CRS-PatternList3, or lte-CRS-PatternList4 is configured; and

-    the higher-layer parameter dmrs-AdditionalPosition is equal to 'pos1' and \(l_{0} = 3\); and

-    the UE has indicated it is capable of additionalDMRS-DL-Alt

For PDSCH mapping type B

-    if the PDSCH duration \(l_{\text{d}}\) \(\in \left\{ {2,3,4,5,6,7,8,9,10,11,12,13} \right\}\) OFDM symbols for normal cyclic prefix or \(l_{\text{d}} \in \left\{ {2,4,6} \right\}\) OFDM symbols for extended cyclic prefix, and the front-loaded DM-RS of the PDSCH allocation collides with resources reserved for a search space set associated with a CORESET, \(\overline{l}\) shall be incremented such that the first DM-RS symbol occurs immediately after the CORESET and until no collision with any CORESET occurs, and

-    if the PDSCH duration \(l_{\text{d}}\) is 2 symbols, the UE is not expected to receive a DM-RS symbol beyond the second symbol;

-    if the PDSCH duration \(l_{d}\) is 5 symbols and if one additional single-symbol DMRS is configured, the UE only expects the additional DM-RS to be transmitted on the 5th symbol when the front-loaded DM-RS symbol is in the 1st symbol of the PDSCH duration, otherwise the UE should expect that the additional DM-RS is not transmitted;

-    if the PDSCH duration \(l_{\text{d}}\) is 7 symbols for normal cyclic prefix or 6 symbols for extended cyclic prefix:

-    if one additional single-symbol DM-RS is configured, the UE only expects the additional DM-RS to be transmitted on the 5th or 6th symbol when the front-loaded DM-RS symbol is in the 1st or 2nd symbol, respectively, of the PDSCH duration, otherwise the UE should expect that the additional DM-RS is not transmitted;

-    if the PDSCH duration \(l_{\text{d}}\) \(\in \left\{ {5,6,7,8,9,10,11,12,13} \right\}\) OFDM symbols, the UE is not expected to receive the front-loaded DM-RS beyond the 4th symbol;

-    if the PDSCH duration \(l_{\text{d}}\) is 12 or 13 symbols, the UE is not expected to receive DM-RS mapped to symbol 12 or later in the slot;

-    for all values of the PDSCH duration \(l_{\text{d}}\) other than 2, 5, and 7 symbols, the UE is not expected to receive DM-RS beyond the \(\left( l_{\text{d}} - 1 \right)\):th symbol;

-    if the PDSCH duration \(l_{\text{d}}\) is less than or equal to 4 OFDM symbols, only single-symbol DM-RS is supported.

-    if the higher-layer parameter lte-CRS-ToMatchAround, lte-CRS-PatternList1, lte-CRS-PatternList2, lte-CRS-PatternList3, or lte-CRS-PatternList4 is configured, the PDSCH duration \(l_{\text{d}} = 10\) symbols for normal cyclic prefix, the subcarrier spacing configuration \(\mu = 0\), single-symbol DM-RS is configured, and at least one PDSCH DM-RS symbol in the PDSCH allocation collides with a symbol containing resource elements as indicated by the higher-layer parameter lte-CRS-ToMatchAround, lte-CRS-PatternList1, lte-CRS-PatternList2, lte-CRS-PatternList3, or lte-CRS-PatternList4, then \(\bar{l}\) shall be incremented by one in all slots.

The time-domain index \(l'\) and the supported antenna ports \(p\) are given by Table 7.4.1.1.2-5 where

-    single-symbol DM-RS is used if the higher-layer parameter maxLength in the DMRS-DownlinkConfig IE is not configured;

-    single-symbol or double-symbol DM-RS is determined by the associated DCI if the higher-layer parameter maxLength in the DMRS-DownlinkConfig IE is equal to 'len2';

-    basic or enhanced DM-RS multiplexing is controlled by the higher-layer parameter dmrs-TypeEnh.

In absence of CSI-RS configuration, and unless otherwise configured, the UE may assume PDSCH DM-RS and SS/PBCH block to be quasi co-located with respect to Doppler shift, Doppler spread, average delay, delay spread, and, when applicable, spatial Rx parameters. Unless specified otherwise, the UE may assume that the PDSCH DM-RS within the same CDM group are quasi co-located with respect to Doppler shift, Doppler spread, average delay, delay spread, and spatial Rx (when applicable). The UE may assume that DMRS ports associated with a TCI state as described in clause 5.1.6.2 of [6, TS 38.214] of a PDSCH are QCL with QCL Type A, Type D (when applicable) and average gain.

The UE may assume that no DM-RS collides with the SS/PBCH block.

Table 7.4.1.1.2-1: Parameters for PDSCH DM-RS configuration type 1.

\[\mathbf{p}\]

CDM group \(\mathbf{\lambda}\)

\[\mathbf{\Delta}\]

\[\begin{bmatrix} {\mathbf{w}_{\text{f}}(0)} & \ldots & {\mathbf{w}_{\text{f}}(3)} \end{bmatrix}\]

\[\begin{bmatrix} {\mathbf{w}_{\text{t}}(0)} & {\mathbf{w}_{\text{t}}(1)} \end{bmatrix}\]

1000

0

0

\[\begin{bmatrix} {+ 1} & {+ 1} & {+ 1} & {+ 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

1001

0

0

\[\begin{bmatrix} {+ 1} & {- 1} & {+ 1} & {- 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

1002

1

1

\[\begin{bmatrix} {+ 1} & {+ 1} & {+ 1} & {+ 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

1003

1

1

\[\begin{bmatrix} {+ 1} & {- 1} & {+ 1} & {- 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

1004

0

0

\[\begin{bmatrix} {+ 1} & {+ 1} & {+ 1} & {+ 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

1005

0

0

\[\begin{bmatrix} {+ 1} & {- 1} & {+ 1} & {- 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

1006

1

1

\[\begin{bmatrix} {+ 1} & {+ 1} & {+ 1} & {+ 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

1007

1

1

\[\begin{bmatrix} {+ 1} & {- 1} & {+ 1} & {- 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

1008

0

0

\[\begin{bmatrix} {+ 1} & {+ 1} & {- 1} & {- 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

1009

0

0

\[\begin{bmatrix} {+ 1} & {- 1} & {- 1} & {+ 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

1010

1

1

\[\begin{bmatrix} {+ 1} & {+ 1} & {- 1} & {- 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

1011

1

1

\[\begin{bmatrix} {+ 1} & {- 1} & {- 1} & {+ 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

1012

0

0

\[\begin{bmatrix} {+ 1} & {+ 1} & {- 1} & {- 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

1013

0

0

\[\begin{bmatrix} {+ 1} & {- 1} & {- 1} & {+ 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

1014

1

1

\[\begin{bmatrix} {+ 1} & {+ 1} & {- 1} & {- 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

1015

1

1

\[\begin{bmatrix} {+ 1} & {- 1} & {- 1} & {+ 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

 

Table 7.4.1.1.2-2: Parameters for PDSCH DM-RS configuration type 2.

\[\mathbf{p}\]

CDM group \(\mathbf{\lambda}\)

\[\mathbf{\Delta}\]

\[\begin{bmatrix} {\mathbf{w}_{\text{f}}(0)} & \ldots & {\mathbf{w}_{\text{f}}(3)} \end{bmatrix}\]

\[\begin{bmatrix} {\mathbf{w}_{\text{t}}(0)} & {\mathbf{w}_{\text{t}}(1)} \end{bmatrix}\]

1000

0

0

\[\begin{bmatrix} {+ 1} & {+ 1} & {+ 1} & {+ 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

1001

0

0

\[\begin{bmatrix} {+ 1} & {- 1} & {+ 1} & {- 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

1002

1

2

\[\begin{bmatrix} {+ 1} & {+ 1} & {+ 1} & {+ 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

1003

1

2

\[\begin{bmatrix} {+ 1} & {- 1} & {+ 1} & {- 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

1004

2

4

\[\begin{bmatrix} {+ 1} & {+ 1} & {+ 1} & {+ 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

1005

2

4

\[\begin{bmatrix} {+ 1} & {- 1} & {+ 1} & {- 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

1006

0

0

\[\begin{bmatrix} {+ 1} & {+ 1} & {+ 1} & {+ 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

1007

0

0

\[\begin{bmatrix} {+ 1} & {- 1} & {+ 1} & {- 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

1008

1

2

\[\begin{bmatrix} {+ 1} & {+ 1} & {+ 1} & {+ 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

1009

1

2

\[\begin{bmatrix} {+ 1} & {- 1} & {+ 1} & {- 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

1010

2

4

\[\begin{bmatrix} {+ 1} & {+ 1} & {+ 1} & {+ 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

1011

2

4

\[\begin{bmatrix} {+ 1} & {- 1} & {+ 1} & {- 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

1012

0

0

\[\begin{bmatrix} {+ 1} & {+ 1} & {- 1} & {- 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

1013

0

0

\[\begin{bmatrix} {+ 1} & {- 1} & {- 1} & {+ 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

1014

1

2

\[\begin{bmatrix} {+ 1} & {+ 1} & {- 1} & {- 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

1015

1

2

\[\begin{bmatrix} {+ 1} & {- 1} & {- 1} & {+ 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

1016

2

4

\[\begin{bmatrix} {+ 1} & {+ 1} & {- 1} & {- 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

1017

2

4

\[\begin{bmatrix} {+ 1} & {- 1} & {- 1} & {+ 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {+ 1} \end{bmatrix}\]

1018

0

0

\[\begin{bmatrix} {+ 1} & {+ 1} & {- 1} & {- 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

1019

0

0

\[\begin{bmatrix} {+ 1} & {- 1} & {- 1} & {+ 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

1020

1

2

\[\begin{bmatrix} {+ 1} & {+ 1} & {- 1} & {- 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

1021

1

2

\[\begin{bmatrix} {+ 1} & {- 1} & {- 1} & {+ 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

1022

2

4

\[\begin{bmatrix} {+ 1} & {+ 1} & {- 1} & {- 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

1023

2

4

\[\begin{bmatrix} {+ 1} & {- 1} & {- 1} & {+ 1} \end{bmatrix}\]

\[\begin{bmatrix} {+ 1} & {- 1} \end{bmatrix}\]

 

Table 7.4.1.1.2-3: PDSCH DM-RS positions \(\overline{l}\) for single-symbol DM-RS.

\(l_{\text{d}}\) in symbols

DM-RS positions \(\overline{l}\)

PDSCH mapping type A

PDSCH mapping type B

dmrs-AdditionalPosition

dmrs-AdditionalPosition

pos0

pos1

pos2

pos3

pos0

pos1

pos2

pos3

2

-

-

-

-

\(\ell_0\)

\(\ell_0\)

\[l_{0}\]

\[l_{0}\]

3

\(\ell_0\)

\(\ell_0\)

\(\ell_0\)

\(\ell_0\)

\[l_{0}\]

\[l_{0}\]

\[l_{0}\]

\[l_{0}\]

4

\(\ell_0\)

\(\ell_0\)

\(\ell_0\)

\(\ell_0\)

\(\ell_0\)

\(\ell_0\)

\[l_{0}\]

\[l_{0}\]

5

\(\ell_0\)

\(\ell_0\)

\(\ell_0\)

\(\ell_0\)

\[l_{0}\]

\[l_{0},4\]

\[l_{0},4\]

\[l_{0},4\]

6

\(\ell_0\)

\(\ell_0\)

\(\ell_0\)

\(\ell_0\)

\(l_{0}\)

\(l_{0,4}\)

\[l_{0},4\]

\[l_{0},4\]

7

\(\ell_0\)

\(\ell_0\)

\(\ell_0\)

\(\ell_0\)

\(\ell_0\)

\(l_{0,4}\)

\[l_{0},4\]

\[l_{0},4\]

8

\(\ell_0\)

\(\ell_0\), 7

\(\ell_0\), 7

\(\ell_0\), 7

\[l_{0}\]

\[l_{0},6\]

\[l_{0},3,6\]

\[l_{0},3,6\]

9

\(\ell_0\)

\(\ell_0\), 7

\(\ell_0\), 7

\(\ell_0\), 7

\[l_{0}\]

\[l_{0},7\]

\[l_{0},4,7\]

\[l_{0},4,7\]

10

\(\ell_0\)

\(\ell_0\), 9

\(\ell_0\), 6, 9

\(\ell_0\), 6, 9

\[l_{0}\]

\[l_{0},7\]

\[l_{0},4,7\]

\[l_{0},4,7\]

11

\(\ell_0\)

\(\ell_0\), 9

\(\ell_0\), 6, 9

\(\ell_0\), 6, 9

\[l_{0}\]

\[l_{0},8\]

\[l_{0},4,8\]

\[l_{0},3,6,9\]

12

\(\ell_0\)

\(\ell_0\), 9

\(\ell_0\), 6, 9

\(\ell_0\), 5, 8, 11

\[l_{0}\]

\[l_{0},9\]

\[l_{0},5,9\]

\[l_{0},3,6,9\]

13

\(\ell_0\)

\(\ell_0\), \(l_{1}\)

\(\ell_0\), 7, 11

\(\ell_0\), 5, 8, 11

\[l_{0}\]

\[l_{0},9\]

\[l_{0},5,9\]

\[l_{0},3,6,9\]

14

\(\ell_0\)

\(\ell_0\), \(l_{1}\)

\(\ell_0\), 7, 11

\(\ell_0\), 5, 8, 11

-

-

-

-

 

Table 7.4.1.1.2-4: PDSCH DM-RS positions \(\overline{l}\) for double-symbol DM-RS.

\(l_{\text{d}}\) in symbols

DM-RS positions \(\overline{l}\)

PDSCH mapping type A

PDSCH mapping type B

dmrs-AdditionalPosition

dmrs-AdditionalPosition

pos0

pos1

pos2

pos0

pos1

pos2

<4

 

 

 

-

-

 

4

\(\ell_0\)

\(\ell_0\)

 

-

-

 

5

\(\ell_0\)

\(\ell_0\)

 

\[l_{0}\]

\[l_{0}\]

 

6

\(\ell_0\)

\(\ell_0\)

 

\(l_{0}\)

\(l_{0}\)

 

7

\(\ell_0\)

\(\ell_0\)

 

\(\ell_0\)

\(\ell_0\)

 

8

\(\ell_0\)

\(\ell_0\)

 

\[l_{0}\]

\[l_{0},5\]

 

9

\(\ell_0\)

\(\ell_0\)

 

\[l_{0}\]

\[l_{0},5\]

 

10

\(\ell_0\)

\(\ell_0\), 8

 

\[l_{0}\]

\[l_{0},7\]

 

11

\(\ell_0\)

\(\ell_0\), 8

 

\[l_{0}\]

\[l_{0},7\]

 

12

\(\ell_0\)

\(\ell_0\), 8

 

\[l_{0}\]

\[l_{0},8\]

 

13

\(\ell_0\)

\(\ell_0\), 10

 

\[l_{0}\]

\[l_{0},8\]

 

14

\(\ell_0\)

\(\ell_0\), 10

 

-

-

 

 

Table 7.4.1.1.2-5: PDSCH DM-RS time index \(\mathbf{l}\mathbf{'}\) and antenna ports \(\mathbf{p}\).

DM-RS multiplexing

DM-RS duration

\[\mathbf{l}\mathbf{'}\]

Supported antenna ports \(\mathbf{p}\)

Configuration type 1

Configuration type 2

Basic

single-symbol DM-RS

0

1000 – 1003

1000 – 1005

double-symbol DM-RS

0, 1

1000 – 1007

1000 – 1011

Enhanced

single-symbol DM-RS

0

1000 – 1003, 1008 – 1011

1000 – 1005, 1012 – 1017

double-symbol DM-RS

0, 1

1000 – 1015

1000 – 1023

 

7.4.1.2     Phase-tracking reference signals for PDSCH #

7 .4.1.2.1    Sequence generation #

The phase-tracking reference signal for subcarrier \(k\) is given by

-    If the higher-layer parameter dmrs-TypeEnh is configured

    \(r_{k} = r\left( {4m + k'} \right)\)

-    otherwise

    \(r_{k} = r\left( {2m + k'} \right)\)

where \(r( \bullet )\) is the demodulation reference signal given by clause 7.4.1.1.2 at position \(l_{0}\) and subcarrier \(k\).

7.4.1.2 .2    Mapping to physical resources #

The UE shall assume phase-tracking reference signals being present only in the resource blocks used for the PDSCH, and only if the procedure in [6, TS 38.214] indicates phase-tracking reference signals being used.

If present, the UE shall assume the PDSCH PT-RS is scaled by a factor \(\beta_{\text{PT-RS}}\) to conform with the transmission power specified in clause 4.1 of [6, TS 38.214] and mapped to resource elements \(\left( {k,l} \right)_{p,\mu}\)according to

\[a_{k,l}^{(p,\mu)} = \beta_{\text{PT-RS}}r_{k}\]

when all the following conditions are fulfilled

-    \(l\) is within the OFDM symbols allocated for the PDSCH transmission

-    resource element \(\left( {k,l} \right)_{p,\mu}\) is not used for DM-RS, non-zero-power CSI-RS (except for those configured for mobility measurements or with resourceType in corresponding CSI-ResourceConfig configured as 'aperiodic'), zero-power CSI-RS, SS/PBCH block, a detected PDCCH according to clause 5.1.4.1 of [6, TS38.214], or is declared as 'not available' by clause 5.1.4 of [6, TS 38.214]

The set of time indices \(l\) defined relative to the start of the PDSCH allocation is defined by

1.    set \(i = 0\) and \(l_{\text{ref}} = 0\)

2.    if any symbol in the interval \(\max\limits_{}{\left( {l_{\text{ref}} + \left( {i - 1} \right)L_{\text{PT-RS}} + 1,l_{\text{ref}}} \right),\ldots,l_{\text{ref}} + iL_{\text{PT-RS}}}\) overlaps with a symbol used for DM-RS according to clause 7.4.1.1.2

-    set \(i = 1\)

-    set \(l_{\text{ref}}\) to the symbol index of the DM-RS symbol in case of a single-symbol DM-RS and to the symbol index of the second DM-RS symbol in case of a double-symbol DM-RS

-    repeat from step 2 as long as \(l_{\text{ref}} + iL_{\text{PT-RS}}\) is inside the PDSCH allocation

3.    add \(l_{\text{ref}} + iL_{\text{PT-RS}}\) to the set of time indices for PT-RS

4.    increment \(i\) by one

5.    repeat from step 2 above as long as \(l_{\text{ref}} + iL_{\text{PT-RS}}\) is inside the PDSCH allocation

where \(L_{\text{PT-RS}} \in \left\{ {1,2,4} \right\}\).

For the purpose of PT-RS mapping, the resource blocks allocated for PDSCH transmission are numbered from 0 to \(N_{RB}-1\) from the lowest scheduled resource block to the highest. The corresponding subcarriers in this set of resource blocks are numbered in increasing order starting from the lowest frequency from 0 to \(N_{sc}^{\mathrm{RB}}\,N_{\mathrm{RB}}-1\). The subcarriers to which the UE shall assume the PT-RS is mapped are given by

\(k = k_{\mathrm{ref}}^{\mathrm{RE}} + \bigl(i K_{\mathrm{PT\!-\!RS}} + k_{\mathrm{ref}}^{\mathrm{RB}}\bigr) N_{\mathrm{sc}}^{\mathrm{RB}} k_{\mathrm{ref}}^{\mathrm{RB}} = \begin{cases} n_{\mathrm{RNTI}} \bmod K_{\mathrm{PT\!-\!RS}}, & \text{if } N_{\mathrm{RB}} \bmod K_{\mathrm{PT\!-\!RS}} = 0, \\ n_{\mathrm{RNTI}} \bmod \bigl(N_{\mathrm{RB}} \bmod K_{\mathrm{PT\!-\!RS}}\bigr), & \text{otherwise} \end{cases}\)

where

-    \(i = 0,1,2,\ldots\)

-    \(k_{\mathrm{ref}}^{\mathrm{RE}}\) is given by Table 7.4.1.2.2-1 for the DM-RS port associated with the PT-RS port according to clause 5.1.6.3 in [6, TS 38.214]. If the higher-layer parameter resourceElementOffset in the PTRS-DownlinkConfig IE is not configured, the column corresponding to 'offset00' shall be used.

-    \(n_{\mathrm{RNTI}}\) is the RNTI associated with the DCI scheduling the transmission

-    \(N_{RB}\) is the number of resource blocks scheduled

-    \(K_{\text{PT-RS}} \in \left\{ 2,4 \right\}\) is given by [6, TS 38.214].

Table 7.4.1.2.2-1: The parameter \(k_{\mathrm{ref}}^{\mathrm{RE}}\).

DM-RS antenna port

\(p\)

\(k_{\mathrm{ref}}^{\mathrm{RE}}\)

DM-RS Configuration type 1

DM-RS Configuration type 2

resourceElementOffset

resourceElementOffset

offset00

offset01

offset10

offset11

offset00

offset01

offset10

offset11

1000

0

2

6

8

0

1

6

7

1001

2

4

8

10

1

6

7

0

1002

1

3

7

9

2

3

8

9

1003

3

5

9

11

3

8

9

2

1004

-

-

-

-

4

5

10

11

1005

-

-

-

-

5

10

11

4

1008

4

6

10

0

-

-

-

-

1009

6

8

0

2

-

-

-

-

1010

5

7

11

1

-

-

-

-

1011

7

9

1

3

-

-

-

-

1012

-

-

-

-

6

7

0

1

1013

-

-

-

-

7

0

1

6

1014

-

-

-

-

8

9

2

3

1015

-

-

-

-

9

2

3

8

1016

-

-

-

-

10

11

4

5

1017

-

-

-

-

11

4

5

10

 

7 .4.1.3    Demodulation reference signals for PDCCH #

7.4.1.3.1     Sequence generation #

The UE shall assume the reference-signal sequence \(r_{l}(m)\) for OFDM symbol \(l\) is defined by

\(r_{l}(m)=\frac{1}{\sqrt{2}}\left(1-2\cdot c(2m)\right)+j\,\frac{1}{\sqrt{2}}\left(1-2\cdot c(2m+1)\right)\).

where the pseudo-random sequence \(c(i)\) is defined in clause 5.2.1. The pseudo-random sequence generator shall be initialized with

    \(c_{\text{init}} = \left( {2^{17}\left( {N_{\text{symb}}^{\text{slot}}n_{\text{s,f}}^{\mu} + l + 1} \right)\left( {2N_{\text{ID}} + 1} \right) + {2N}_{\text{ID}}} \right)\text{mod}2^{31}\)

where \(l\) is the OFDM symbol number within the slot, \(n_{\text{s,f}}^{\mu}\) is the slot number within a frame, and

-    \(N_{\text{ID}} \in \left\{ {0,1,\ldots,65535} \right\}\) is given by the higher-layer parameter pdcch-DMRS-ScramblingID if provided;

-    \(N_{\text{ID}} \in \left\{ {0,1,\ldots,65535} \right\}\) is given by the higher-layer parameter pdcch-DMRS-ScramblingID if configured for a common search space in a common MBS frequency resource;

-    \(N_{\text{ID}} = N_{\text{ID}}^{\text{cell}}\) otherwise.

7.4.1.3.2     Mapping to physical resources #

The UE shall assume the sequence \(r_{l}(m)\) is mapped to resource elements \(\left( {k,l} \right)_{p,\mu}\) according to

\(\begin{aligned} a_{k,l}^{(p,\mu)} &= \beta_{\mathrm{DMRS}}^{\mathrm{PDCCH}} \cdot r_l(3n + k') \\ k &= n N_{sc}^{\mathrm{RB}} + 4k' + 1 \\ k' &= 0,1,2 \\ n &= 0,1,\ldots \end{aligned}\)

where the following conditions are fulfilled

-    they are within the resource element groups constituting the PDCCH the UE attempts to decode if the higher-layer parameter precoderGranularity equals sameAsREG-bundle,

-    all resource-element groups within the set of contiguous resource blocks in the CORESET where the UE attempts to decode the PDCCH if the higher-layer parameter precoderGranularity equals allContiguousRBs.

The reference point for \(k\) is

-    subcarrier 0 of the lowest-numbered resource block in the CORESET if the CORESET is configured by the PBCH or by the controlResourceSetZero field in the PDCCH-ConfigCommon IE,

-    subcarrier 0 in common resource block 0 otherwise

The quantity \(l\) is the OFDM symbol number within the slot.

The antenna port \(p = 2000\).

A UE not attempting to detect a PDCCH in a CORESET shall not make any assumptions on the presence or absence of DM-RS in the CORESET.

In absence of CSI-RS configuration, and unless otherwise configured, the UE may assume PDCCH DM-RS and SS/PBCH block to be quasi co-located with respect to Doppler shift, Doppler spread, average delay, delay spread, and, when applicable, spatial Rx parameters.

7 .4.1.4    Demodulation reference signals for PBCH #

7.4.1.4.1     Sequence generation #

The UE shall assume the reference-signal sequence \(r(m)\) for an SS/PBCH block is defined by

\(r(m)=\frac{1}{\sqrt{2}}\left(1-2\cdot c(2m)\right)+j\frac{1}{\sqrt{2}}\left(1-2\cdot c(2m+1)\right)\)

where \(c(n)\) is given by clause 5.2. The scrambling sequence generator shall be initialized at the start of each SS/PBCH block occasion with

\(c_{\mathrm{init}} = 2^{11}(\bar{i}_{\mathrm{SSB}}+1)\left(\left\lfloor \frac{N_{\mathrm{ID}}^{\mathrm{cell}}}{4} \right\rfloor + 1\right) + 2^{6}(\bar{i}_{\mathrm{SSB}}+1) + \left(N_{\mathrm{ID}}^{\mathrm{cell}} \bmod 4\right)\)

where

-    for \({\bar{L}}_{\max} = 4\), \(\overline{i}_{\mathrm{SSB}} = i_{\mathrm{SSB}} + 4 n_{\mathrm{hf}}\) where \(n_{hf}\) is the number of the half-frame in which the PBCH is transmitted in a frame with \(n_{bf}=0\) for the first half-frame in the frame and \(n_{hf}=1\) for the second half-frame in the frame, and \(i_{SSB}\) is the two least significant bits of the candidate SS/PBCH block index as defined in [5, TS 38.213]

-    for \({\bar{L}}_{\max} > 4\), \(\overline{i}_{\mathrm{SSB}}=i_{\mathrm{SSB}}\) where \(i_{SSB}\) is the three least significant bits of the candidate SS/PBCH block index as defined in [5, TS 38.213]

with \({\bar{L}}_{\max}\) being the maximum number of candidate SS/PBCH blocks in a half frame, as described in [5, TS 38.213].

7.4.1.4.2     Mapping to physical resources #

Mapping to physical resources is described in clause 7.4.3.

7 .4.1.5    CSI reference signals #

7.4.1.5.1     General #

Zero-power (ZP) and non-zero-power (NZP) CSI-RS are defined

-    for a non-zero-power CSI-RS configured by the NZP-CSI-RS-Resource IE or by the CSI-RS-Resource-Mobility field in the CSI-RS-ResourceConfigMobility IE or by the TRS-ResourceSet IE, the sequence shall be generated according to clause 7.4.1.5.2 and mapped to resource elements according to clause 7.4.1.5.3

-    for a zero-power CSI-RS configured by the ZP-CSI-RS-Resource IE, the UE shall assume that the resource elements defined in clause 7.4.1.5.3 are not used for PDSCH transmission subject to clause 5.1.4.2 of [6, TS 38.214]. The UE performs the same measurement/reception on channels/signals except PDSCH regardless of whether they collide with ZP CSI-RS or not.

7.4.1.5. 2    Sequence generation #

The UE shall assume the reference-signal sequence \(r(m)\) is defined by

\(r(m)=\frac{1}{\sqrt{2}}\left(1-2\cdot c(2m)\right)+j\frac{1}{\sqrt{2}}\left(1-2\cdot c(2m+1)\right)\)

where the pseudo-random sequence \(c(i)\) is defined in clause 5.2.1. The pseudo-random sequence generator shall be initialised with

\[c_{\text{init}} = \left( {2^{10}\left( {N_{\text{symb}}^{\text{slot}}n_{\text{s,f}}^{\mu} + l + 1} \right)\left( {2n_{\text{ID}} + 1} \right) + n_{\text{ID}}} \right)\text{mod}2^{31}\]

at the start of each OFDM symbol where \(n_{\text{s,f}}^{\mu}\) is the slot number within a radio frame, \(l\) is the OFDM symbol number within a slot, and \(n_{\mathrm{ID}}\) equals the higher-layer parameter scramblingID or sequenceGenerationConfig.

7.4.1.5. 3    Mapping to physical resources #

For each CSI-RS configured, the UE shall assume the sequence \(r(m)\) being mapped to resources elements \(\left( {k,l} \right)_{p,\mu}\) according to

ak,lp,μ=βCSIRSwfkq'wtlq'rl,ns,fm'm'=nα+kq'+kqρ/NscRBk=nNscRB+kq+kq'l=lq+lq'α=ρfor N=12ρfor N>1n=0,1,

when the following conditions are fulfilled:

-    the resource element \(\left( {k,l} \right)_{p,\mu}\) is within the resource blocks occupied by the CSI-RS resource for which the UE is configured

The reference point for \(k = 0\) is subcarrier 0 in common resource block 0.

The value of \(\rho\) is given by the higher-layer parameter density in the CSI-RS-ResourceMapping IE or the CSI-RS-CellMobility IE.

The number of ports \(N\) per CSI-RS resource is given by the higher-layer parameter nrofPorts and the number of CSI-RS resources by the total number of CSI-RS ports \(N_{\text{tot}}\)

-    if \(N_{\text{tot}} \in \left\{ {1,2,4,8,12,16,24,32} \right\}\), there is one CSI-RS resource with \(N\) CSI-RS ports, \(q = 0\), and \(N_{\text{tot}} = N\);

-    if \(N_{\text{tot}} \in \left\{ {48,64,128} \right\}\), the aggregated resource for the \(N_{\text{tot}} = KN\) ports is formed by aggregating \(K\) CSI-RS resources with \(N\) CSI-RS ports each, where the possible combinations of \(N_{\text{tot}}\), \(K\), and \(N\) are given by Table 7.4.1.5.3-6, and where \(q = 0,\ldots,K - 1\) is the CSI-RS resource index within the aggregated CSI-RS resource.

For NZP CSI-RS configured by the TRS-ResourceSet IE, the density \(\rho = 3\) and number of ports \(X = 1\).

The UE is not expected to receive CSI-RS and DM-RS on the same resource elements.

The UE shall assume \(\beta_{\mathrm{CSIRS}}>0\) for a non-zero-power CSI-RS where \(\beta_{\mathrm{CSIRS}}\) is selected="selected" such that the power offset specified by the higher-layer parameter powerControlOffsetSS in the NZP-CSI-RS-Resource IE or in the TRS-ResourceSet IE, if provided, is fulfilled.

The quantities \(k_{q}'\), \(l_{q}'\), \(w_{\text{f}}\left( k_{q}' \right)\), and \(w_{\text{t}}\left( l_{q}' \right)\) are given by Tables 7.4.1.5.3-1 to 7.4.1.5.3-5 where each \(\left( {{\bar{k}}_{q},{\bar{l}}_{q}} \right)\) in a given row of Table 7.4.1.5.3-1 corresponds to a CDM group of size 1 (no CDM) or size 2, 4, or 8. The CDM type is provided by the higher layer parameter cdm-Type in the CSI-RS-ResourceMapping IE. For NZP CSI-RS configured by the TRS-ResourceSet IE, the CDM type is 'noCDM'. The indices \(k_{i}'\) and \(l_{i}'\) index resource elements within a CDM group.

The time-domain locations \(l_{0} \in \left\{ {0,1,\ldots,13} \right\}\) and \(l_{1} \in \left\{ {2,3,\ldots,12} \right\}\) are provided by the higher-layer parameters firstOFDMSymbolInTimeDomain and firstOFDMSymbolInTimeDomain2, respectively, in the CSI-RS-ResourceMapping IE or the CSI-RS-ResourceConfigMobility IE and defined relative to the start of a slot. For NZP CSI-RS configured by TRS-ResourceSet IE, the time-domain location \(l_{0} \in \left\{ {0,1,\ldots,13} \right\}\) is provided by the higher-layer parameter firstOFDMSymbolInTimeDomain or firstOFDMSymbolInTimeDomain+4.

The frequency-domain location is given by a bitmap provided by the higher-layer parameter frequencyDomainAllocation in the CSI-RS-ResourceMapping IE, the CSI-RS-ResourceConfigMobility IE, or the TRS-ResourceSet IE, with the bitmap and value of \(k_{i}\) in Table 7.4.1.5.3-1 given by

-    \(\left[ b_{3} \cdots b_{0} \right]\), \(k_{i - 1} = f(i)\) for row 1 of Table 7.4.1.5.3-1

-    \(\left[ b_{11} \cdots b_{0} \right]\), \(k_{i - 1} = f(i)\) for row 2 of Table 7.4.1.5.3-1

-    \(\left[b_{2}\cdots b_{0}\right]\), \(k_{i - 1} = 4f(i)\) for row 4 of Table 7.4.1.5.3-1

-    \( [b_{5}\cdots b_{0}] \), \(k_{i - 1} = 2f(i)\) for all other cases

where \(f(i)\) is the bit number of the \(i^{\text{th}}\) bit in the bitmap set to one, repeated across every \(\left\lceil {1/\rho} \right\rceil\) of the resource blocks configured for CSI-RS reception by the UE. The starting position and number of the resource blocks in which the UE shall assume that CSI-RS is transmitted are given by the higher-layer parameters freqBand and density in the CSI-RS-ResourceMapping IE for the bandwidth part given by the higher-layer parameter BWP-Id in the CSI-ResourceConfig IE or given by the higher-layer parameters nrofPRBs in the CSI-RS-CellMobility IE where the the startPRB given by csi-rs-MeasurementBW is relative to common resource block 0. For NZP CSI-RS configured by TRS-ResourceSet IE, the starting position and number of the resource blocks in which the CSI-RS can be transmitted are given by the higher-layer parameters nrofRBs, and startingRB in the TRS-ResourceSet IE, where startingRB is relative to common resource block 0 and the density \(\rho = 3\).

The UE shall assume that a CSI-RS is transmitted using antenna ports \(p\) numbered according to

    \(p = 3000 + p'\)

where

-    if the number of CSI-RS ports \(N_{\text{tot}} \in \left\{ {1,2,4,8,12,16,24,32} \right\}\)

    \(p' = \overset{\sim}{p}\)

-    if the number of CSI-RS ports \(N_{\text{tot}} \in \left\{ {48,64,128} \right\}\)

-    if the higher-layer parameter portMappingMethod equals ‘method1’ and \(N_{1}/K\) is an integer where \(N_{1}\) is as defined in Table 5.2.2.2.1a-1 of [6, TS 38.214]

    \(p' = \begin{cases} {\overset{\sim}{p} + qN/2} & {0 \leq \overset{\sim}{p} < N/2} \\ {\overset{\sim}{p} + \left( {K + q - 1} \right)N/2} & {N/2 \leq \overset{\sim}{p} < N} \end{cases}\)

    where \(q = 0,1,\ldots,K - 1\) is the number of the CSI-RS resource within the aggregated CSI-RS resource.

-    if the higher-layer parameter portMappingMethod equals ‘method2’

    \(p' = N_{2}\left\lfloor {\overset{\sim}{p}/N_{2}^{'}} \right\rfloor + qN_{2}^{'}\text{+}\left( {\overset{\sim}{p}\text{mod}N_{2}^{'}} \right)\)

    \(N_{2}^{'}{} = {N_{2}/K}\)

    where \(q = 0,1,\ldots,K - 1\) is the number of the CSI-RS resource within the aggregated CSI-RS resource, \(N_{2}/K\) is an integer, and \(N_{2}\) is as defined in Table 5.2.2.2.1a-1 of [6, TS 38.214].

where

\[\begin{matrix} {\overset{\sim}{p} = s + jL} \\ {j = 0,1,\ldots,{N/L} - 1} \\ {s = 0,1,\ldots,L - 1} \end{matrix}\]

and where \(s\) is the sequence index provided by Tables 7.4.1.5.3-2 to 7.4.1.5.3-5, \(L \in \left\{ {1,2,4,8} \right\}\) is the CDM group size, and \(N\) is the number of CSI-RS ports. The CDM group index \(j\) given in Table 7.4.1.5.3-1 corresponds to the time/frequency locations \(\left( {{\bar{k}}_{q},{\bar{l}}_{q}} \right)\) for a given row of the table. The CDM groups are numbered in order of increasing frequency domain allocation first and then increasing time domain allocation.

For a CSI-RS resource configured as periodic or semi-persistent by the higher-layer parameter resourceType, configured by the higher-layer parameter CSI-RS-CellMobility, or configured by the higher-layer parameter TRS-ResourceSet, the UE shall assume that the CSI-RS is transmitted in slots satisfying

\[\left( {N_{\text{slot}}^{\text{frame,}\mu}n_{\text{f}} + n_{\text{s,f}}^{\mu} - T_{\text{offset}}} \right)\text{mod}T_{\text{CSI-RS}} = 0\]

where the periodicity \(T_{\text{CSI-RS}}\) (in slots) and slot offset \(T_{\text{offset}}\) are obtained from the higher-layer parameter CSI-ResourcePeriodicityAndOffset, slotConfig, periodicityAndOffset. The UE shall assume that CSI-RS is transmitted in a candidate slot as described in clause 11.1 of [5, TS 38.213], clause 10.4B of [5, TS 38.213].

The UE may assume that antenna ports within a CSI-RS resource are quasi co-located with QCL Type A, Type D (when applicable), and average gain.

 

Table 7.4.1.5.3-1: CSI-RS locations within a slot.

Row

Ports\(\mathbf{N}\)

Density \(\mathbf{\rho}\)

cdm-Type

\[\left( {{\bar{k}}_{q},{\bar{l}}_{q}} \right)\]

CDM group index \(j\)

\[\mathbf{k}_{\mathbf{q}}\mathbf{'}\]

\[\mathbf{l}_{\mathbf{q}}\mathbf{'}\]

1

1

3

noCDM

\(\left( {k_{0},l_{0}} \right)\), \(\left( {k_{0} + 4,l_{0}} \right)\), \(\left( {k_{0} + 8,l_{0}} \right)\)

0,0,0

0

0

2

1

1, 0.5

noCDM

\(\left( {k_{0},l_{0}} \right)\),

0

0

0

3

2

1, 0.5

fd-CDM2

\(\left( {k_{0},l_{0}} \right)\),

0

0, 1

0

4

4

1

fd-CDM2

\(\left( {k_{0},l_{0}} \right)\),\(\left( {k_{0} + 2,l_{0}} \right)\)

0,1

0, 1

0

5

4

1

fd-CDM2

\(\left( {k_{0},l_{0}} \right)\),\(\left( {k_{0},l_{0} + 1} \right)\)

0,1

0, 1

0

6

8

1

fd-CDM2

\(\left( {k_{0},l_{0}} \right)\), \(\left( {k_{1},l_{0}} \right)\), \(\left( {k_{2},l_{0}} \right)\), \(\left( {k_{3},l_{0}} \right)\)

0,1,2,3

0, 1

0

7

8

1

fd-CDM2

\(\left( {k_{0},l_{0}} \right)\), \(\left( {k_{1},l_{0}} \right)\),\(\left( {k_{0},l_{0} + 1} \right)\), \(\left( {k_{1},l_{0} + 1} \right)\)

0,1,2,3

0, 1

0

8

8

1

cdm4-FD2-TD2

\(\left( {k_{0},l_{0}} \right)\), \(\left( {k_{1},l_{0}} \right)\)

0,1

0, 1

0, 1

9

12

1

fd-CDM2

\(\left( {k_{0},l_{0}} \right)\), \(\left( {k_{1},l_{0}} \right)\), \(\left( {k_{2},l_{0}} \right)\), \(\left( {k_{3},l_{0}} \right)\),\(\left( {k_{4},l_{0}} \right)\), \(\left( {k_{5},l_{0}} \right)\)

0,1,2,3,4,5

0, 1

0

10

12

1

cdm4-FD2-TD2

\(\left( {k_{0},l_{0}} \right)\), \(\left( {k_{1},l_{0}} \right)\), \(\left( {k_{2},l_{0}} \right)\)

0,1,2

0, 1

0, 1

11

16

1, 0.5

fd-CDM2

\(\left( {k_{0},l_{0}} \right)\), \(\left( {k_{1},l_{0}} \right)\), \(\left( {k_{2},l_{0}} \right)\), \(\left( {k_{3},l_{0}} \right)\),\(\left( {k_{0},l_{0} + 1} \right)\), \(\left( {k_{1},l_{0} + 1} \right)\), \(\left( {k_{2},l_{0} + 1} \right)\), \(\left( {k_{3},l_{0} + 1} \right)\)

0,1,2,3,

4,5,6,7

0, 1

0

12

16

1, 0.5

cdm4-FD2-TD2

\(\left( {k_{0},l_{0}} \right)\), \(\left( {k_{1},l_{0}} \right)\), \(\left( {k_{2},l_{0}} \right)\), \(\left( {k_{3},l_{0}} \right)\)

0,1,2,3

0, 1

0, 1

13

24

1, 0.5

fd-CDM2

\(\left( {k_{0},l_{0}} \right)\), \(\left( {k_{1},l_{0}} \right)\), \(\left( {k_{2},l_{0}} \right)\), \(\left( {k_{0},l_{0} + 1} \right)\), \(\left( {k_{1},l_{0} + 1} \right)\), \(\left( {k_{2},l_{0} + 1} \right)\),\(\left( {k_{0},l_{1}} \right)\), \(\left( {k_{1},l_{1}} \right)\), \(\left( {k_{2},l_{1}} \right)\), \(\left( {k_{0},l_{1} + 1} \right)\), \(\left( {k_{1},l_{1} + 1} \right)\), \(\left( {k_{2},l_{1} + 1} \right)\)

0,1,2,3,4,5,

6,7,8,9,10,11

0, 1

0

14

24

1, 0.5

cdm4-FD2-TD2

\(\left( {k_{0},l_{0}} \right)\), \(\left( {k_{1},l_{0}} \right)\), \(\left( {k_{2},l_{0}} \right)\), \(\left( {k_{0},l_{1}} \right)\), \(\left( {k_{1},l_{1}} \right)\), \(\left( {k_{2},l_{1}} \right)\)

0,1,2,3,4,5

0, 1

0, 1

15

24

1, 0.5

cdm8-FD2-TD4

\(\left( {k_{0},l_{0}} \right)\), \(\left( {k_{1},l_{0}} \right)\), \(\left( {k_{2},l_{0}} \right)\)

0,1,2

0, 1

0, 1, 2, 3

16

32

1, 0.5

fd-CDM2

\(\left( {k_{0},l_{0}} \right)\), \(\left( {k_{1},l_{0}} \right)\), \(\left( {k_{2},l_{0}} \right)\), \(\left( {k_{3},l_{0}} \right)\),\(\left( {k_{0},l_{0} + 1} \right)\), \(\left( {k_{1},l_{0} + 1} \right)\), \(\left( {k_{2},l_{0} + 1} \right)\), \(\left( {k_{3},l_{0} + 1} \right)\), \(\left( {k_{0},l_{1}} \right)\), \(\left( {k_{1},l_{1}} \right)\), \(\left( {k_{2},l_{1}} \right)\), \(\left( {k_{3},l_{1}} \right)\), \(\left( {k_{0},l_{1} + 1} \right)\), \(\left( {k_{1},l_{1} + 1} \right)\), \(\left( {k_{2},l_{1} + 1} \right)\), \(\left( {k_{3},l_{1} + 1} \right)\)

0,1,2,3,

4,5,6,7,

8,9,10,11,

12,13,14,15

0, 1

0

17

32

1, 0.5

cdm4-FD2-TD2

\(\left( {k_{0},l_{0}} \right)\), \(\left( {k_{1},l_{0}} \right)\), \(\left( {k_{2},l_{0}} \right)\), \(\left( {k_{3},l_{0}} \right)\), \(\left( {k_{0},l_{1}} \right)\), \(\left( {k_{1},l_{1}} \right)\), \(\left( {k_{2},l_{1}} \right)\), \(\left( {k_{3},l_{1}} \right)\)

0,1,2,3,4,5,6,7

0, 1

0, 1

18

32

1, 0.5

cdm8-FD2-TD4

\(\left( {k_{0},l_{0}} \right)\), \(\left( {k_{1},l_{0}} \right)\), \(\left( {k_{2},l_{0}} \right)\), \(\left( {k_{3},l_{0}} \right)\)

0,1,2,3

0,1

0,1, 2, 3

 

Table 7.4.1.5.3-2: The sequences \(\mathbf{w}_{\text{f}}\left( \mathbf{k}_{\mathbf{q}}\mathbf{'} \right)\) and \(\mathbf{w}_{\text{t}}\left( \mathbf{l}_{\mathbf{q}}\mathbf{'} \right)\) for cdm-Type equal to 'noCDM'.

Index

\[\mathbf{w}_{\text{f}}(0)\]

\[\mathbf{w}_{\text{t}}(0)\]

0

1

1

 

Table 7.4.1.5.3-3: The sequences \(\mathbf{w}_{\text{f}}\left( \mathbf{k}_{\mathbf{q}}\mathbf{'} \right)\) and \(\mathbf{w}_{\text{t}}\left( \mathbf{l}_{\mathbf{q}}\mathbf{'} \right)\) for cdm-Type equal to 'fd-CDM2'.

Index

\[\begin{bmatrix} {\mathbf{w}_{\text{f}}(0)} & {\mathbf{w}_{\text{f}}(1)} \end{bmatrix}\]

\[\mathbf{w}_{\text{t}}(0)\]

0

\(\begin{bmatrix}+1 & +1\end{bmatrix}\)

1

1

\(\begin{bmatrix}+1&-1\end{bmatrix}\)

1

 

Table 7.4.1.5.3-4: The sequences \(\mathbf{w}_{\text{f}}\left( \mathbf{k}_{\mathbf{q}}\mathbf{'} \right)\) and \(\mathbf{w}_{\text{t}}\left( \mathbf{l}_{\mathbf{q}}\mathbf{'} \right)\) for cdm-Type equal to 'cdm4-FD2-TD2'.

Index

\[\begin{bmatrix} {\mathbf{w}_{\text{f}}(0)} & {\mathbf{w}_{\text{f}}(1)} \end{bmatrix}\]

\[\begin{bmatrix} {\mathbf{w}_{\text{t}}(0)} & {\mathbf{w}_{\text{t}}(1)} \end{bmatrix}\]

0

\(\begin{bmatrix}+1 & +1\end{bmatrix}\)

\(\begin{bmatrix}+1 & +1\end{bmatrix}\)

1

\(\begin{bmatrix}+1&-1\end{bmatrix}\)

\(\begin{bmatrix}+1 & +1\end{bmatrix}\)

2

\(\begin{bmatrix}+1 & +1\end{bmatrix}\)

\(\begin{bmatrix}+1&-1\end{bmatrix}\)

3

\(\begin{bmatrix}+1&-1\end{bmatrix}\)

\(\begin{bmatrix}+1&-1\end{bmatrix}\)

 

Table 7.4.1.5.3-5: The sequences \(\mathbf{w}_{\text{f}}\left( \mathbf{k}_{\mathbf{q}}\mathbf{'} \right)\) and \(\mathbf{w}_{\text{t}}\left( \mathbf{l}_{\mathbf{q}}\mathbf{'} \right)\) for cdm-Type equal to 'cdm8-FD2-TD4'.

Index

\[\begin{bmatrix} {\mathbf{w}_{\text{f}}(0)} & {\mathbf{w}_{\text{f}}(1)} \end{bmatrix}\]

\[\begin{bmatrix} {\mathbf{w}_{\text{t}}(0)} & {\mathbf{w}_{\text{t}}(1)} & {\mathbf{w}_{\text{t}}(2)} & {\mathbf{w}_{\text{t}}(3)} \end{bmatrix}\]

0

\(\begin{bmatrix}+1 & +1\end{bmatrix}\)

\(\left[ +1\quad +1\quad +1\quad +1 \right]\)

1

\(\begin{bmatrix}+1&-1\end{bmatrix}\)

\(\left[ +1\quad +1\quad +1\quad +1 \right]\)

2

\(\begin{bmatrix}+1 & +1\end{bmatrix}\)

\(\begin{bmatrix}+1&-1&+1&-1\end{bmatrix}\)

3

\(\begin{bmatrix}+1&-1\end{bmatrix}\)

\(\begin{bmatrix}+1&-1&+1&-1\end{bmatrix}\)

4

\(\begin{bmatrix}+1 & +1\end{bmatrix}\)

\(\begin{bmatrix}+1 & +1 & -1 & -1\end{bmatrix}\)

5

\(\begin{bmatrix}+1&-1\end{bmatrix}\)

\(\begin{bmatrix}+1 & +1 & -1 & -1\end{bmatrix}\)

6

\(\begin{bmatrix}+1 & +1\end{bmatrix}\)

\(\begin{bmatrix}+1 & -1 & -1 & +1\end{bmatrix}\)

7

\(\begin{bmatrix}+1&-1\end{bmatrix}\)

\(\begin{bmatrix}+1 & -1 & -1 & +1\end{bmatrix}\)

 

Table 7.4.1.5.3-6: The supported combinations of \(\mathbf{N}_{\text{tot}}\), \(\mathbf{K}\), and \(\mathbf{N}\) when the number of CSI-RS ports is 48, 64, or 128.

\[\mathbf{N}_{\text{tot}}\]

\[\mathbf{K}\]

\[\mathbf{N}\]

48

2

24

48

3

16

64

4

16

64

2

32

128

4

32

 

7.4.1.6     RIM reference signals #

7.4.1.6.1     General #

RIM-RS can be used by an gNB to measure inter-cell interference and to provide information about the experienced interference to other gNBs. Up to two different types of RIM-RS can be configured where

-    the first RIM-RS type can be used to convey information,

-    the second RIM-RS type depends on configuration only.

7.4.1.6.2     Sequence generation #

The RIM-RS receiver shall assume the reference-signal sequence \(r(m)\) is defined by

    \(r(m) = \frac{1}{\sqrt[{}]{2}}\left( {1 - 2c\left( {2m} \right)} \right) + j\frac{1}{\sqrt[{}]{2}}\left( {1 - 2c\left( {2m + 1} \right)} \right)\)

where the pseudo-random sequence \(c(m)\) is defined in clause 5.2.1. The pseudo-random sequence generator shall be initialised with

    \(c_{\text{init}} = \left( {2^{10}f\left( n_{\text{t}}^{\text{RIM}} \right) + n_{\text{SCID}}} \right)\text{mod}2^{31}\)

where

-    \(n_{\text{SCID}} \in \left\{ {0,1,\ldots,2^{10} - 1} \right\}\) is given by clause 7.4.1.6.4.4;

-    \(f\left( n_{\text{t}}^{\text{RIM}} \right) = \sum\limits_{i = 0}^{20}{2^{i}\bar{c}}(i)\) where the pseudo-random sequence \(\bar{c}(i)\) is given by clause 5.2.1, initialized with \({\bar{c}}_{\text{init}}(i) = \left( {\gamma n_{\text{t}}^{\text{RIM}} + \delta} \right)\text{mod}2^{31}\) where the multiplier factor \(\gamma \in \left\{ {0,1,\ldots,2^{31} - 1} \right\}\) and the offset \(\delta \in \left\{ {0,1,\ldots,2^{31} - 1} \right\}\);

-    \(n_{\text{t}}^{\text{RIM}} = \left\lfloor {\left( {t_{\text{RS}}^{\text{RIM}} - t_{\text{ref}}^{\text{RIM}}} \right)/T_{\text{per}}^{\text{RIM}}} \right\rfloor\) is the number of RIM-RS transmission periods since \(t_{\text{ref}}^{\text{RIM}}\) where

-    \(t_{\text{RS}}^{\text{RIM}} - t_{\text{ref}}^{\text{RIM}}\) is the time in seconds relative to \(t_{\text{ref}}^{\text{RIM}}\) of 00:00:00 on 1 January 1900, calculated as continuous time without leap second and traceable to a common time reference, and

-    \(T_{\text{per}}^{\text{RIM}} = {N_{\text{slot}}^{P_{t}}/\left( {1000 \cdot 2^{\mu}} \right)}\) is the RIM-RS transmission periodicity in seconds assuming that the first RIM-RS transmission period starts at \(t_{\text{ref}}^{\text{RIM}}\), and where \(N_{\text{slot}}^{P_{t}}\) is given by clause 7.4.1.6.4.2.

7.4.1.6.3     Mapping to physical resources #

The RIM-RS receiver shall assume the reference signal being mapped to physical resources according to

    \(a_{k}^{(p,\text{RIM})} = \beta_{\text{RIM}}r(k)\)

    \(k = 0,1,\ldots,L_{\text{RIM}} - 1\)

where \(\beta_{\text{RIM}}\) is an amplitude scaling factor in order to control the RIM-RS transmission power and \(p\) is the antenna port. Baseband signal generation shall be done according to clause 5.3.3.

The starting position \(l_{0}\) for RIM-RS type \(i \in \left\{ 1,2 \right\}\) in slot \(n_{\text{s,f}}^{\mu}\) in a frame is given by

    \(l_{0} = T_{\text{offset}}^{\text{UD,RIM}}\text{mod}N_{\text{symb}}^{\text{slot}}\)

in slots satisfying

    \(\left( {1024N_{\text{slot}}^{\text{frame,}\mu}{\bar{n}}_{\text{f}}^{\text{RIM}} + N_{\text{slot}}^{\text{frame,}\mu}n_{\text{f}}^{\text{RIM}} + n_{\text{s,f}}^{\mu} - \left( {{\bar{T}}_{\text{offset}} + \left\lfloor {T_{\text{offset}}^{\text{UD,RIM}}/N_{\text{symb}}^{\text{slot}}} \right\rfloor} \right)} \right)\text{mod}N_{\text{slot}}^{P_{\text{t}}} = 0\)

where

-    \({\bar{n}}_{\text{f}}^{\text{RIM}}\text{∈}\left\{ {0,1,\ldots,{N_{\text{slot}}^{P_{t}}/\left( {1024N_{\text{slot}}^{\text{frame,}\mu}} \right)} - 1} \right\}\) counts the number of times the SFN periods within the RIM-RS transmission period;

-    \(T_{\text{offset}}^{\text{UD,RIM}} = N_{\text{ref}}^{\text{UD,RIM}} - N_{\text{symb,ref}}^{\text{RIM,}i}\) where \(N_{\text{ref}}^{\text{UD,RIM}} \in \left\{ {2,3,\ldots,20 \cdot 2 \cdot 14 - 1} \right\}\) is the symbol offset of the reference point after the starting boundary of the uplink-downlink switching period in which the RIM-RS is mapped to and \(N_{\text{symb,ref}}^{\text{RIM,}i}\) is obtained as described in clause 7.4.1.6.4.2;

-    \(N_{\text{slot}}^{P_{t}}\) is the total number of slots in a RIM-RS transmission period as defined in clause 7.4.1.6.4.2;

-    \({\bar{T}}_{\text{offset}}\) is the slot offset of the uplink-downlink switching period with index \(i_{\text{t}}^{\text{RIM}}\) with respect to the starting boundary of the RIM-RS transmission period and is defined in clause 7.4.1.6.4.2;

-    \(P_{\text{t}}\) is the RIM-RS transmission periodicity in units of uplink-downlink switching period as defined in clause 7.4.1.6.4.2.

7.4.1.6.4     RIM-RS configuration #
7.4.1.6.4.1     General #

A resource for RIM-RS transmission is defined by the indices \(i_{\text{t}}^{\text{RIM}} \in \left\{ {0,1,\ldots,P_{\text{t}} - 1} \right\}\), \(i_{\text{f}}^{\text{RIM}} \in \left\{ {0,1,\ldots,N_{\text{f}}^{\text{RIM}} - 1} \right\}\), and \(i_{\text{s}}^{\text{RIM}} \in \left\{ {0,1,\ldots,N_{\text{s}}^{\text{RIM,}i} - 1} \right\}\) used as indices into configured lists of time, frequency, and sequence parameters, respectively.

All RIM-RS resources occupy the same number of resource blocks, \(N_{\text{RB}}^{\text{RIM}}\). At most 32 RIM-RS resources can be configured within a 10 ms period.

7.4.1.6.4.2     Time-domain parameters and mapping from \(i_{\text{t}}\) to time-domain parameters #

RIM-RS are transmitted periodically with the RIM-RS transmission period \(P_{\text{t}}\) defined in units of the uplink-downlink switching period determined from one or two configured uplink-downlink periods.

-    If a single uplink-downlink period is configured for RIM-RS purposes,

-    \(P_{\text{t}}\) is the RIM-RS transmission periodicity in terms of uplink-downlink switching periods given by

\[P_{\text{t}} = \left\lceil \frac{2^{\mu}{\bar{P}}_{\text{t}}T_{\text{per},1}^{\text{RIM}}}{1024N_{\text{slot}}^{\text{frame},\mu}} \right\rceil\frac{1024N_{\text{slot}}^{\text{frame},\mu}}{2^{\mu}T_{\text{per},1}^{\text{RIM}}}\]

where \(T_{\text{per},1}^{\text{RIM}} \in \left\{ {0.5,0.625,1,1.25,2,2.5,4,5,10,20} \right\}\) ms;

-    \(N_{\text{slot}}^{P_{t}} = 2^{\mu}P_{\text{t}}T_{\text{per},1}^{\text{RIM}}\) is the total number of slots in a RIM-RS transmission period;

-    \({\bar{T}}_{\text{offset}} = 2^{\mu}i_{\text{t}}^{\text{RIM}}T_{\text{per},1}^{\text{RIM}}\) is the slot offset of the uplink-downlink switching period with index \(i_{\text{t}}^{\text{RIM}}\) with respect to the starting boundary of the RIM-RS transmission period

-    If two uplink-downlink periods are configured for RIM-RS purposes,

-    \(P_{\text{t}}\) is the RIM-RS transmission periodicity in terms of \(P_{\text{t}}/2\) pairs of uplink-downlink switching periods and is given by

\[P_{\text{t}} = \left\lceil \frac{2^{\mu}{\bar{P}}_{\text{t}}{\left( {T_{\text{per},1}^{\text{RIM}} + T_{\text{per},2}^{\text{RIM}}} \right)/2}}{1024N_{\text{slot}}^{\text{frame},\mu}} \right\rceil\frac{1024N_{\text{slot}}^{\text{frame},\mu}}{2^{\mu}{\left( {T_{\text{per},1}^{\text{RIM}} + T_{\text{per},2}^{\text{RIM}}} \right)/2}}\]

    where each pair consists of a first period of \(T_{\text{per},1}^{\text{RIM}} \in \left\{ {0.5,0.625,1,1.25,2,2.5,3,4,5,10,20} \right\}\) ms and a second period of \(T_{\text{per},2}^{\text{RIM}} \in \left\{ {0.5,0.625,1,1.25,2,2.5,3,4,5,10} \right\}\) ms and where \(T_{\text{per},1}^{\text{RIM}} + T_{\text{per},2}^{\text{RIM}}\) divides 20 ms;

-    \(N_{\text{slot}}^{P_{t}} = 2^{\mu}P_{\text{t}}{\left( {T_{\text{per},1}^{\text{RIM}} + T_{\text{per},2}^{\text{RIM}}} \right)/2}\) is the total number of slots in a RIM-RS transmission period;

-    \({\bar{T}}_{\text{offset}} = 2^{\mu}\left\lfloor {i_{\text{t}}^{\text{RIM}}/2} \right\rfloor\left( {T_{\text{per},1}^{\text{RIM}} + T_{\text{per},2}^{\text{RIM}}} \right) + 2^{\mu}\left( {i_{\text{t}}^{\text{RIM}}\text{mod}2} \right)T_{\text{per},1}^{\text{RIM}}\) is the slot offset of the uplink-downlink switching period with index \(i_{\text{t}}^{\text{RIM}}\) with respect to the starting boundary of the RIM-RS transmission period

The intermediate quantity \({\bar{P}}_{\text{t}}\) is given by

\[{\bar{P}}_{\text{t}} = \left\{ \begin{matrix} {\left\lceil \frac{N_{\text{setID}}^{\text{RIM,1}}}{N_{\text{f}}^{\text{RIM}}N_{\text{s}}^{\text{RIM,1}}} \right\rceil R_{1} + \left\lceil \frac{N_{\text{setID}}^{\text{RIM,2}}}{N_{\text{f}}^{\text{RIM}}N_{\text{s}}^{\text{RIM,2}}} \right\rceil R_{2}} & {\text{if}\text{EnoughIndication}\text{is disabled}} \\ {\left\lceil \frac{2N_{\text{setID}}^{\text{RIM,1}}}{N_{\text{f}}^{\text{RIM}}N_{\text{s}}^{\text{RIM,1}}} \right\rceil R_{1} + \left\lceil \frac{N_{\text{setID}}^{\text{RIM,2}}}{N_{\text{f}}^{\text{RIM}}N_{\text{s}}^{\text{RIM,2}}} \right\rceil R_{2}} & {\text{if}\text{EnoughIndication}\text{is enabled}} \end{matrix} \right.\]

where

-    \(N_{\text{setID}}^{\text{RIM,1}}\) and \(N_{\text{setID}}^{\text{RIM,2}}\) are the total number of setIDs for RIM-RS type 1 and RIM-RS type 2, respectively;

-    \(N_{\text{f}}^{\text{RIM}} \in \left\{ {1,2,4} \right\}\) is the number of candidate frequency resources configured in the network;

-    \(N_{\text{s}}^{\text{RIM,}i} \in \left\{ {1,2,\ldots,8} \right\}\) is the number of candidate sequences assigned for RIM-RS type \(i \in \left\{ 1,2 \right\}\) in the network;

-    \(R_{1}\) and \(R_{2}\) are the number of consecutive uplink-downlink switching periods for RIM-RS type 1 and RIM-RS type 2, respectively. If near-far functionality is not configured, \(R_{i} \in \left\{ {1,2,4} \right\}\), otherwise \(R_{i} \in \left\{ {2,4,8} \right\}\) and the first and second half of the \(R_{i}\) consecutive uplink-downlink switching periods are for near functionality and far functionality, respectively.

The quantity \(N_{\text{symb,ref}}^{\text{RIM,}i}\) is obtained from entry \(\bar{r}\) in a list of configured symbol offsets for RIM-RS \(i\).

7.4.1.6.4.3     Frequency-domain parameters and mapping from \(i_{\text{f}}\) to frequency-domain parameters #

The frequency-domain parameter \(k_{1}\) in clause 5.3.3 is the frequency offset relative to a configured reference point for RIM-RS and is obtained from entry \(i_{\text{f}}^{\text{RIM}}\) in a list of configured frequency offsets expressed in units of resource blocks.

The number of candidate frequency resources configured in the network, \(N_{\text{f}}^{\text{RIM}}\), shall fulfil

\[N_{\text{f}}^{\text{RIM}} \leq \left\lfloor \frac{N_{\text{grid}}^{\text{size},\mu}N_{\text{RB}}^{\text{sc}} \cdot 2^{\mu} \cdot 15}{40 \cdot 10^{3}} \right\rfloor + \left\lfloor \frac{N_{\text{grid}}^{\text{size},\mu}N_{\text{RB}}^{\text{sc}} \cdot 2^{\mu} \cdot 15}{80 \cdot 10^{3}} \right\rfloor + 1\]

If \(N_{\text{f}}^{\text{RIM}} > 1\), the frequency difference between any pair of configured frequency offsets in the list is not smaller than \(N_{\text{RB}}^{\text{RIM}}\).

The number of resource blocks for RIM-RS is given by

\[\begin{array}{ll} {N_{\text{RB}}^{\text{RIM}} = \min\left( {96,N_{\text{grid,DL}}^{\text{size,}\text{μ}}} \right)} & {\text{for}\mu = 0} \\ {N_{\text{RB}}^{\text{RIM}} \in \left\{ {\min\left( {48,N_{\text{grid,DL}}^{\text{size,}\text{μ}}} \right),\min\left( {96,N_{\text{grid,DL}}^{\text{size,}\text{μ}}} \right)} \right\}} & {\text{for}\mu = 1} \end{array}\]

7.4.1.6.4.4     Sequence parameters and mapping from \(i_{\text{s}}\) to sequence parameters #

The scrambling identity \(n_{\text{SCID}}\) clause 7.4.1.6.2 is obtained from entry \(i_{\text{s}}^{\text{RIM}}\) in a list of configured scrambling identities.

7.4.1.6.4.5     Mapping between resource triplet and set ID #

The resource indices \(i_{\text{t}}^{\text{RIM}}\), \(i_{\text{f}}^{\text{RIM}}\), and \(i_{\text{s}}^{\text{RIM}}\) are determined from the index \(\bar{r}\) in the set ID \(n_{\text{setID}}\) according to

\[\begin{matrix} {i_{\text{t}}^{\text{RIM}} = T_{\text{start}} + \left( {\left\lfloor \frac{n_{\text{setID}}}{N_{\text{s}}^{\text{RIM}}} \right\rfloor\text{mod}N_{\text{t}}^{\text{RIM}}} \right)R_{i} + \bar{r}} \\ {i_{\text{f}}^{\text{RIM}} = \left( {\left\lfloor \frac{n_{\text{setID}}}{N_{\text{t}}^{\text{RIM}}N_{\text{s}}^{\text{RIM}}} \right\rfloor\text{mod}N_{\text{f}}^{\text{RIM}}} \right)} \\ {i_{\text{s}}^{\text{RIM}} = S_{\text{start}} + \left( {n_{\text{setID}}\text{mod}N_{\text{s}}^{\text{RIM}}} \right)} \end{matrix}\]

where

-    \(N_{\text{t}}^{\text{RIM}}\) is given by

\[N_{\text{t}}^{\text{RIM}} = \left\{ \begin{matrix} \left\lceil \frac{N_{\text{setID}}^{\text{RIM,1}}}{N_{\text{f}}^{\text{RIM}}N_{\text{s}}^{\text{RIM,1}}} \right\rceil & {\text{for RIM-RS type 1 and if}\text{EnoughIndication}\text{is disabled}} \\ \left\lceil \frac{2N_{\text{setID}}^{\text{RIM,1}}}{N_{\text{f}}^{\text{RIM}}N_{\text{s}}^{\text{RIM,1}}} \right\rceil & {\text{for RIM-RS type 1 and if}\text{EnoughIndication}\text{is enabled}} \\ \left\lceil \frac{N_{\text{setID}}^{\text{RIM,2}}}{N_{\text{f}}^{\text{RIM}}N_{\text{s}}^{\text{RIM,2}}} \right\rceil & \text{for RIM-RS type 2} \end{matrix} \right.\]

-    \(N_{\text{f}}^{\text{RIM}} \in \left\{ {1,2,4} \right\}\) is the number of candidate frequency resources configured in the network;

-    \(N_{\text{s}}^{\text{RIM}}\) is the number of sequence candidates for the current RIM-RS resource given by

\[N_{\text{s}}^{\text{RIM}} = \left\{ \begin{matrix} N_{\text{s}}^{\text{RIM,1}} & {\text{for RIM-RS type 1 and if}\text{EnoughIndication}\text{is disabled}} \\ {N_{\text{s}}^{\text{RIM,1}}/2} & {\text{for RIM-RS type 1 and if}\text{EnoughIndication}\text{is enabled}} \\ N_{\text{s}}^{\text{RIM,2}} & \text{for RIM-RS type 2} \end{matrix} \right.\]

-    \(T_{\text{start}}\) is the starting time offset given by

\[T_{\text{start}} = \left\{ \begin{matrix} 0 & \text{for RIM-RS type 1} \\ {\left\lceil \frac{N_{\text{setID}}^{\text{RIM,1}}}{N_{\text{f}}^{\text{RIM}}N_{\text{s}}^{\text{RIM,1}}} \right\rceil R_{1}} & {\text{for RIM-RS type 2 and if}\text{EnoughIndication}\text{is disabled="disabled"}} \\ {\left\lceil \frac{2N_{\text{setID}}^{\text{RIM,1}}}{N_{\text{f}}^{\text{RIM}}N_{\text{s}}^{\text{RIM,1}}} \right\rceil R_{1}} & {\text{for RIM-RS type 2 and if}\text{EnoughIndication}\text{is enabled}} \end{matrix} \right.\]

-    \(S_{\text{start}}\) is given by

\[S_{\text{start}} = \left\{ \begin{matrix} {N_{\text{s}}^{\text{RIM,1}}/2} & {\text{if}\text{EnoughIndication}\text{is enabled and 'enough mitigation' is to be indicated}} \\ 0 & \text{otherwise} \end{matrix} \right.\]

where \(N_{\text{s}}^{\text{RIM,1}}\) is the number of candidate sequences assigned for RIM-RS type 1

-    \(R_{i}\) is the number of consecutive uplink-downlink periods for RIM-RS type \(i\) as given by clause 7.4.1.6.4.2;

-    \(\bar{r} \in \left\{ {0,1,\ldots,R_{i} - 1} \right\}\).

The set ID is determined from the resource triplet according to

\[n_{\text{setID}} = \left( {i_{\text{s}}^{\text{RIM}} - S_{\text{start}}} \right) + N_{\text{s}}^{\text{RIM}}\left\lfloor \frac{{i_{\text{t}}^{\text{RIM}} - T}_{\text{start}}}{R_{i}} \right\rfloor + N_{\text{t}}^{\text{RIM}}N_{\text{s}}^{\text{RIM}}i_{\text{f}}^{\text{RIM}}\]

7.4.1.7     Positioning reference signals #

7.4.1.7.1     General #

A positioning frequency layer consists of one or more downlink PRS resource sets, each of which consists of one or more downlink PRS resources as described in [6, TS 38.214].

7.4.1.7.2     Sequence generation #

The UE shall assume the reference-signal sequence \(r(m)\) is defined by

\[r(m) = \frac{1}{\sqrt[{}]{2}}\left( {1 - 2c\left( {2m} \right)} \right) + j\frac{1}{\sqrt[{}]{2}}\left( {1 - 2c\left( {2m + 1} \right)} \right)\]

where the pseudo-random sequence \(c(i)\) is defined in clause 5.2.1. The pseudo-random sequence generator shall be initialised with

\[c_{\text{init}} = \left( {2^{22}\left\lfloor \frac{n_{\text{ID,seq}}^{\text{PRS}}}{1024} \right\rfloor + 2^{10}\left( {N_{\text{symb}}^{\text{slot}}n_{\text{s,f}}^{\mu} + l + 1} \right)\left( {2\left( {n_{\text{ID,seq}}^{\text{PRS}}\text{mod}1024} \right) + 1} \right) + \left( {n_{\text{ID,seq}}^{\text{PRS}}\text{mod}1024} \right)} \right)\text{mod}2^{31}\]

where \(n_{\text{s,f}}^{\mu}\) is the slot number, the downlink PRS sequence ID \(n_{\text{ID,seq}}^{\text{PRS}} \in \left\{ {0,1,\ldots,4095} \right\}\) is given by the higher-layer parameter dl-PRS-SequenceID, and \(l\) is the OFDM symbol within the slot to which the sequence is mapped.

For each downlink PRS resource configured, the UE shall assume the sequence \(r(m)\) is scaled with a factor \(\beta_{\text{PRS}}\) and mapped to resources elements \(\left( {k,l} \right)_{p,\mu}\) according to

\[\begin{matrix} {a_{k,l}^{({p,\mu})} = \beta_{\text{PRS}}r(m)} \\ {m = 0,1,\ldots} \\ {k = mK_{\text{comb}}^{\text{PRS}} + \left( {\left( {k_{\text{offset}}^{\text{PRS}} + k'} \right)\text{mod}K_{\text{comb}}^{\text{PRS}}} \right)} \\ {l = l_{\text{start}}^{\text{PRS}},l_{\text{start}}^{\text{PRS}} + 1,\ldots,l_{\text{start}}^{\text{PRS}} + L_{\text{PRS}} - 1} \end{matrix}\]

when the following conditions are fulfilled:

-    the resource element \(\left( {k,l} \right)_{p,\mu}\) is within the resource blocks occupied by the downlink PRS resource for which the UE is configured;

-    the symbol \(l\) is not used by any SS/PBCH block used by a serving cell for downlink PRS transmitted from the same serving cell or any SS/PBCH block from a non-serving cell whose time frequency location is provided to the UE by higher layers for downlink PRS transmitted from the same non-serving cell;

-    the slot number satisfies the conditions in clause 7.4.1.7.4.

and where

-    the antenna port \(p = 5000\)

-    \(l_{\text{start}}^{\text{PRS}}\) is the first symbol of the downlink PRS within a slot and given by the higher-layer parameter dl-PRS-ResourceSymbolOffset;

-    the size of the downlink PRS resource in the time domain \(L_{\text{PRS}} \in \left\{ {1,2,4,6,12} \right\}\) is given by the higher-layer parameter dl-PRS-NumSymbols;

-    the comb size \(K_{\text{comb}}^{\text{PRS}} \in \left\{ {2,4,6,12} \right\}\) is given by the higher-layer parameter dl-PRS-CombSizeN-AndReOffset for a downlink PRS resource configured for RTT-based propagation delay compensation, otherwise by the higher-layer parameter dl-PRS-CombSizeN such that the combination \(\left\{ {L_{\text{PRS}},K_{\text{comb}}^{\text{PRS}}} \right\}\) is one of {1, 2}, {2, 2},{4, 2}, {6, 2}, {12, 2}, {1, 4}, {4, 4}, {12, 4}, {1, 6}, {6, 6}, {12, 6}, {1, 12} and {12, 12};

-    the resource-element offset \(k_{\text{offset}}^{\text{PRS}} \in \left\{ {0,1,\ldots,K_{\text{comb}}^{\text{PRS}} - 1} \right\}\) is obtained from the higher-layer parameter dl-PRS-CombSizeN-AndReOffset;

-    the quantity \(k'\) is given by Table 7.4.1.7.3-1.

If the downlink PRS resource is configured for RTT based propagation delay compensation as described in clause 9 of [6, TS 38.214], the reference point for \(k = 0\) is subcarrier 0 in common resource block 0; Otherwise, the reference point for \(k = 0\) is the location of the point A of the positioning frequency layer, in which the downlink PRS resource is configured where point A is given by the higher-layer parameter dl-PRS-PointA.

Table 7.4.1.7.3-1: The frequency offset \(\mathbf{k}\mathbf{'}\) as a function of \(\mathbf{l} - \mathbf{l}_{\text{start}}^{\text{PRS}}\).

\[\mathbf{K}_{\text{comb}}^{\text{PRS}}\]

Symbol number within the downlink PRS resource \(\mathbf{l} - \mathbf{l}_{\text{start}}^{\text{PRS}}\)

0

1

2

3

4

5

6

7

8

9

10

11

2

0

1

0

1

0

1

0

1

0

1

0

1

4

0

2

1

3

0

2

1

3

0

2

1

3

6

0

3

1

4

2

5

0

3

1

4

2

5

12

0

6

3

9

1

7

4

10

2

8

5

11

 

For a downlink PRS resource in a downlink PRS resource set, the UE shall assume the downlink PRS resource being transmitted when the slot and frame numbers fulfil

\[\left( {N_{\text{slot}}^{\text{frame},\mu}n_{\text{f}} + n_{\text{s,f}}^{\mu} - T_{\text{offset}}^{\text{PRS}} - T_{\text{offset,res}}^{\text{PRS}}} \right)\text{mod}T_{\text{per}}^{\text{PRS}} \in \left\{ {iT_{\text{gap}}^{\text{PRS}}} \right\}_{i = 0}^{T_{\text{rep}}^{\text{PRS}} - 1}\]

and one of the following conditions are fulfilled:

-    the higher-layer parameters dl-PRS-MutingOption1 and dl-PRS-MutingOption2 are not provided;

-    the higher-layer parameter dl-PRS-MutingOption1 is provided with bitmap \(\left\{ b^{1} \right\}\) but dl-PRS-MutingOption2 with bitmap \(\left\{ b^{2} \right\}\) is not provided, and bit \(b_{i}^{1}\) is set;

-    the higher-layer parameter dl-PRS-MutingOption2 is provided with bitmap \(\left\{ b^{2} \right\}\) but dl-PRS-MutingOption1 with bitmap \(\left\{ b^{1} \right\}\) is not provided, and bit \(b_{i}^{2}\) is set;

-    the higher-layer parameters dl-PRS-MutingOption1 with bitmap \(\left\{ b^{1} \right\}\) and dl-PRS-MutingOption2 with \(\left\{ b^{2} \right\}\) are both provided, and both bit \(b_{i}^{1}\) and \(b_{i}^{2}\) are set.

where

-    \(b_{i}^{1}\) is bit \(i = \left\lfloor {{\left( {N_{\text{slot}}^{\text{frame},\mu}n_{\text{f}} + n_{\text{s,f}}^{\mu} - T_{\text{offset}}^{\text{PRS}} - T_{\text{offset,res}}^{\text{PRS}}} \right)}/\left( {T_{\text{muting}}^{\text{PRS}}T_{\text{per}}^{\text{PRS}}} \right)} \right\rfloor\text{mod}L\) in the bitmap given by the higher-layer parameter dl-PRS-MutingOption1 where \(L \in \left\{ {2,4,6,8,16,32} \right\}\) is the size of the bitmap;

-    \(b_{i}^{2}\) is bit \(i = \left\lfloor {{\left( {\left( {N_{\text{slot}}^{\text{frame},\mu}n_{\text{f}} + n_{\text{s,f}}^{\mu} - T_{\text{offset}}^{\text{PRS}} - T_{\text{offset,res}}^{\text{PRS}}} \right)\text{mod}T_{\text{per}}^{\text{PRS}}} \right)}/T_{\text{gap}}^{\text{PRS}}} \right\rfloor\text{mod}T_{\text{rep}}^{\text{PRS}}\) in the bitmap given by the higher-layer parameter dl-PRS-MutingOption2;

-    the periodicity \(T_{\text{per}}^{\text{PRS}} \in 2^{\mu}\left\{ {4,5,8,10,16,20,32,40,64,80,160,320,640,1280,2560,5120,10240} \right\}\) and the slot offset \(T_{\text{offset}}^{\text{PRS}} \in \left\{ {0,1,\ldots,T_{\text{per}}^{\text{PRS}} - 1} \right\}\) are given by the higher-layer parameter dl-PRS-Periodicity-and-ResourceSetSlotOffset;

-    the downlink PRS resource slot offset \(T_{\text{offset,res}}^{\text{PRS}}\) is given by the higher-layer parameter dl-PRS-ResourceSlotOffset;

-    the repetition factor \(T_{\text{rep}}^{\text{PRS}} \in \left\{ {1,2,4,6,8,16,32} \right\}\) is given by the higher-layer parameter dl-PRS-ResourceRepetitionFactor;

-    the muting repetition factor \(T_{\text{muting}}^{\text{PRS}}\) is given by the higher-layer parameter dl-PRS-MutingBitRepetitionFactor;

-    the time gap \(T_{\text{gap}}^{\text{PRS}} \in \left\{ {1,2,4,8,16,32} \right\}\) is given by the higher-layer parameter dl-PRS-ResourceTimeGap;

For a downlink PRS resource in a downlink PRS resource set configured for RTT-based propagation delay compensation, the UE shall assume the downlink PRS resource being transmitted as described in clause 9 of [6, TS 38.214]; otherwise, the UE shall assume the downlink PRS resource being transmitted as described in clause 5.1.6.5 of [6, TS 38.214].

7 .4.2    Synchronization signals #

7.4.2.1     Physical-layer cell identities #

There are 1008 unique physical-layer cell identities given by

    \(N_{ID}^{\text{cell}} = 3 N_{ID}^{(1)} + N_{ID}^{(2)}\)

where \(N_{\text{ID}}^{(1)} \in \left\{ {0,1,\ldots,335} \right\}\) and \(N_{\text{ID}}^{(2)} \in \left\{ {0,1,2} \right\}\).

7.4.2. 2    Primary synchronization signal #

7.4.2. 2.1    Sequence generation #

The sequence \(d_{\mathrm{PSS}}(n)\) for the primary synchronization signal is defined by

    \(d_{\mathrm{PSS}}(n)=1-2x(m)\\ m=\bigl(n+43N_{ID}^{(2)}\bigr)\bmod 127\\ 0\le n<127\)

where

    \(x(i+7) = (x(i+4) + x(i)) \bmod 2\)

and

    \(\[ \begin{bmatrix} x(6) & x(5) & x(4) & x(3) & x(2) & x(1) & x(0) \end{bmatrix} = \begin{bmatrix} 1 & 1 & 1 & 0 & 1 & 1 & 0 \end{bmatrix} \]\)

7.4.2. 2.2    Mapping to physical resources #

Mapping to physical resources is described in clause 7.4.3.

7.4.2. 3    Secondary synchronization signal #

7.4.2. 3.1    Sequence generation #

The sequence \(d_{sss}(n)\) for the secondary synchronization signal is defined by

\(\[ d_{sss}(n)=\bigl[1-2\,x_0\bigl((n+m_0)\bmod 127\bigr)\bigr]\bigl[1-2\,x_1\bigl((n+m_1)\bmod 127\bigr)\bigr] \] \[ m_0=15\left\lfloor\frac{N_{\mathrm{ID}}^{(1)}}{112}\right\rfloor+5\,N_{\mathrm{ID}}^{(2)} \] \[ m_1=N_{\mathrm{ID}}^{(1)}\bmod 112 \] \[ 0\le n<127 \]\)

where

    \(\begin{aligned} x_0(i+7) &= \left(x_0(i+4)+x_0(i)\right) \bmod 2,\\ x_1(i+7) &= \left(x_1(i+1)+x_1(i)\right) \bmod 2 \end{aligned}\)

and

    \(\[ \begin{aligned} \begin{bmatrix} x_0(6) & x_0(5) & x_0(4) & x_0(3) & x_0(2) & x_0(1) & x_0(0) \end{bmatrix} &= \begin{bmatrix} 0 & 0 & 0 & 0 & 0 & 0 & 1 \end{bmatrix} \\ \begin{bmatrix} x_1(6) & x_1(5) & x_1(4) & x_1(3) & x_1(2) & x_1(1) & x_1(0) \end{bmatrix} &= \begin{bmatrix} 0 & 0 & 0 & 0 & 0 & 0 & 1 \end{bmatrix} \end{aligned} \]\)

7.4.2. 3.2    Mapping to physical resources #

Mapping to physical resources is described in clause 7.4.3.

7.4.3     SS/PBCH block #

7.4.3.1     Time-frequency structure of an SS/PBCH block #

In the time domain, an SS/PBCH block consists of 4 OFDM symbols, numbered in increasing order from 0 to 3 within the SS/PBCH block, where PSS, SSS, and PBCH with associated DM-RS are mapped to symbols as given by Table 7.4.3.1-1.

In the frequency domain, an SS/PBCH block consists of 240 contiguous subcarriers with the subcarriers numbered in increasing order from 0 to 239 within the SS/PBCH block. The quantities \(k\) and \(l\) represent the frequency and time indices, respectively, within one SS/PBCH block. The UE may assume that the complex-valued symbols corresponding to resource elements denoted as 'Set to 0' in Table 7.4.3.1-1 are set to zero. The quantity \(v\) in Table 7.4.3.1-1 is given by \(v = N_{\text{ID}}^{\text{cell}}\text{mod}4\). The quantity \(k_{\text{SSB}}\) is the subcarrier offset from subcarrier 0 in common resource block \(N_{\text{CRB}}^{\text{SSB}}\) to the lowest-numbered subcarrier of the SS/PBCH block, or the SS/PBCH block after puncturing if applicable, where \(N_{\text{CRB}}^{\text{SSB}}\) is obtained from the higher-layer parameter offsetToPointA.

-    For operation with shared spectrum channel access in FR2-2 and for operation without shared spectrum channel access, the 4 least significant bits of \(k_{\text{SSB}}\) are given by the higher-layer parameter ssb-SubcarrierOffset and for FR1 the most significant bit of \(k_{\text{SSB}}\) is given by \({\bar{a}}_{\bar{A} + 5}\) in the PBCH payload as defined in clause 7.1.1 of [4, TS 38.212].

-    For operation with shared spectrum channel access in FR1, the 4 least significant bits of \({\bar{k}}_{\text{SSB}}\) are given by the higher-layer parameter ssb-SubcarrierOffset and the most significant bit of \({\bar{k}}_{\text{SSB}}\) is given by \({\bar{a}}_{\bar{A} + 5}\) in the PBCH payload as defined in clause 7.1.1 of [4, TS 38.212]. If \({\bar{k}}_{\text{SSB}} \geq 24\), \(k_{\text{SSB}} = {\bar{k}}_{\text{SSB}}\) ; otherwise, \(k_{\text{SSB}} = 2\left\lfloor {{\bar{k}}_{\text{SSB}}/2} \right\rfloor\).

If ssb-SubcarrierOffset is not provided, \(k_{\text{SSB}}\) is derived from the frequency difference between the SS/PBCH block and Point A.

The UE may assume that the complex-valued symbols corresponding to resource elements that are part of a common resource block partially or fully overlapping with an SS/PBCH block, or an SS/PBCH block after puncturing if applicable, and not used for SS/PBCH transmission are set to zero in the OFDM symbols partially or fully overlapping with OFDM symbols where SS/PBCH is transmitted.

For an SS/PBCH block, the UE shall assume

-    antenna port \(p = 4000\) is used for transmission of PSS, SSS, PBCH and DM-RS for PBCH,

-    the same cyclic prefix length and subcarrier spacing for the PSS, SSS, PBCH and DM-RS for PBCH,

-    for SS/PBCH block type A, \(\mu \in \left\{ 0,1 \right\}\) and \(k_{\text{SSB}} \in \left\{ {0,1,2,\ldots,23} \right\}\) with the quantities \(k_{\text{SSB}}\), and \(N_{\text{CRB}}^{\text{SSB}}\) expressed in terms of 15 kHz subcarrier spacing, and

-    for SS/PBCH block type B in FR2-1 and FR2-NTN, \(\mu \in \left\{ 3,4 \right\}\) and \(k_{\text{SSB}} \in \left\{ {0,1,2,\ldots,11} \right\}\) with the quantity \(k_{\text{SSB}}\) expressed in terms of the subcarrier spacing provided by the higher-layer parameter subCarrierSpacingCommon and \(N_{\text{CRB}}^{\text{SSB}}\) expressed in terms of 60 kHz subcarrier spacing;

-    for SS/PBCH block type B in FR2-2, \(\mu \in \left\{ {3,5,6} \right\}\) and \(k_{\text{SSB}} \in \left\{ {0,1,2,\ldots,11} \right\}\) with the quantity \(k_{\text{SSB}}\) expressed in terms of the SS/PBCH block subcarrier spacing and \(N_{\text{CRB}}^{\text{SSB}}\) expressed in terms of 60 kHz subcarrier spacing;

-    the centre of subcarrier 0 of resource block \(N_{\text{CRB}}^{\text{SSB}}\) coincides with the centre of subcarrier 0 of a common resource block with the subcarrier spacing

-    provided by the higher-layer parameter subCarrierSpacingCommon for operation without shared spectrum channel access in FR1, FR2-1 and FR2-NTN; and

-    same as the subcarrier spacing of the SS/PBCH block for operation without shared spectrum access in FR2-2 and for operation with shared spectrum channel access.

-    This common resource block overlaps with subcarrier 0 of the lowest-numbered resource block of the SS/PBCH block, or the SS/PBCH block after puncturing if applicable.

The UE may assume that SS/PBCH blocks transmitted with the same block index on the same center frequency location are quasi co-located with respect to Doppler spread, Doppler shift, average gain, average delay, delay spread, and, when applicable, spatial Rx parameters. The UE shall not assume quasi co-location for any other SS/PBCH block transmissions other than what is specified in [5, TS 38.213].

For cell search on a carrier with a channel bandwidth of 3 MHz, the UE is not expected to receive subcarriers 0 to 47 and 192 to 239 in any of the 4 OFDM symbols of the SS/PBCH block, where the remaining 12 resource blocks form the SS/PBCH block after puncturing.

Table 7.4.3.1-1: Resources within an SS/PBCH block for PSS, SSS, PBCH, and DM-RS for PBCH.

Channel or signal

OFDM symbol number \(l\)relative to the start of an SS/PBCH block<br>

Subcarrier number \(k\)relative to the start of an SS/PBCH block<br>

PSS

0

56, 57, …, 182

SSS

2

56, 57, …, 182

Set to 0

0

0, 1, …, 55, 183, 184, …, 239

2

48, 49, …, 55, 183, 184, …, 191

PBCH

1, 3

0, 1, …, 239

2

0, 1, …, 47, 192, 193, …, 239<br>

DM-RS for PBCH

1, 3

\(0+v,\;4+v,\;8+v,\;\ldots,\;236+v\)

2

\(\[ \begin{aligned} 0+v,\,4+v,\,8+v,\,\ldots,\,44+v\\ 192+v,\,196+v,\,\ldots,\,236+v \end{aligned} \]\)

 

7.4.3.1.1     Mapping of PSS within an SS/PBCH block #

The UE shall assume the sequence of symbols \(d_{\text{PSS}}(0),\,\ldots,\,d_{\text{PSS}}(126)\)constituting the primary synchronization signal to be scaled by a factor \(\beta_{\mathrm{PSS}}\) to conform to the PSS power allocation specified in [5, TS 38.213] and mapped to resource elements \((k,l)_{p,\mu}\) in increasing order of \(k\) where \(k\) and \(l\) are given by Table 7.4.3.1-1 and represent the frequency and time indices, respectively, within one SS/PBCH block.

7.4.3.1.2     Mapping of SSS within an SS/PBCH block #

The UE shall assume the sequence of symbols \(d_{sss}(0),\ldots,d_{sss}(126)\) constituting the secondary synchronization signal to be scaled by a factor \(\beta_{sss}\) and mapped to resource elements \((k,l)_{p,\mu}\) in increasing order of \(k\) where \(k\) and \(l\) are given by Table 7.4.3.1-1 and represent the frequency and time indices, respectively, within one SS/PBCH block.

7.4.3.1.3     Mapping of PBCH and DM-RS within an SS/PBCH block #

The UE shall assume the sequence of complex-valued symbols \(d_{\text{PBCH}}(0),\ldots,d_{\text{PBCH}}\left( {M_{\text{symb}} - 1} \right)\) constituting the physical broadcast channel to be scaled by a factor \(\beta_{\mathrm{PBCH}}\) to conform to the PBCH power allocation specified in [5, TS 38.213] and mapped in sequence starting with \(d_{\mathrm{PBCH}}(0)\) to resource elements \((k,l)_{p,\mu}\) which meet all the following criteria:

-    they are not used for PBCH demodulation reference signals

The mapping to resource elements \((k,l)_{p,\mu}\) not reserved for PBCH DM-RS shall be in increasing order of first the index \(k\) and then the index \(l\), where \(k\) and \(l\) represent the frequency and time indices, respectively, within one SS/PBCH block and are given by Table 7.4.3.1-1.

The UE shall assume the sequence of complex-valued symbols \(r(0),\ldots,r(143)\) constituting the demodulation reference signals for the SS/PBCH block to be scaled by a factor of \(\beta_{\text{PBCH}}^{\text{DM-RS}}\) to conform to the PBCH power allocation specified in [5, TS 38.213] and to be mapped to resource elements \((k,l)_{p,\mu}\) in increasing order of first \(k\) and then \(l\) where \(k\) and \(l\) are given by Table 7.4.3.1-1 and represent the frequency and time indices, respectively, within one SS/PBCH block.

7.4.3.2     Time location of an SS/PBCH block #

The locations in the time domain where a UE shall monitor for a possible SS/PBCH block are described in clause 4.1 of [5, TS 38.213].

7.4.4     Wake-up signal #

7.4.4.1     Sequence generation #

7.4.4.1.1     Generation of \(r_{\text{ZC},m}(n)\) #

The sequence \(r_{\text{ZC},m}(n)\) is defined by

\[r_{\text{ZC},m}(n) = x_{q}\left( {\left( n + n_{\text{cs}} \right)\text{mod}N_{\text{ZC}}} \right)\]

\[x_{q}(i) = e^{- j\frac{\pi qi(i + 1)}{N_{\text{ZC}}}}\]

\[n = 0,1,\ldots,M_{\text{ZC}} - 1\]

where

-    \(N_{\text{ZC}}\) is the largest prime number such that \(N_{\text{ZC}} < M_{\text{ZC}}\)

-    \(M_{\text{ZC}} = {N_{\text{sc}}^{\text{WUS}}/M_{\text{WUS}}}\)

 

The root sequence number \(q \in \left\{ {1,\ldots,N_{\text{ZC}} - 1} \right\}\) is obtained as entry \(\left\lfloor {c_{m}/P} \right\rfloor \in \left\{ 0,1 \right\}\) of the root sequence numbers configured by the higher-layer parameter XXX and the cyclic shift \(n_{\text{cs}}\) is given by

\[\begin{matrix} {n_{\text{cs}} = \left( {c_{m}\text{mod}P} \right)\left\lfloor \frac{N_{\text{ZC}}}{P} \right\rfloor} \end{matrix}\]

\[\begin{matrix} {P = \frac{N_{\text{seq}}}{N_{\text{root}}}} \end{matrix}\]

where

-    \(N_{\text{seq}}\) is the number of sequences configured by the higher-layer parameter XXX

-    \(N_{\text{root}}\epsilon\left\{ 1,2 \right\}\) is the number of root sequence numbers configured by the higher-layer parameter XXX

 

The sequence number \(c_{m} = 0\) if \(L = 1\), otherwise is given by

\[c_{m} = \sum\limits_{i = 0}^{\delta - 1}{f_{1(i + \delta m)}2^{\delta - 1 - i}}\]

\[\delta = \log_{2}L\]

\[m = 0,1,\ldots,\left( {E_{1}/\delta} \right) - 1\]

where

-    \(L\) is given by the higher-layer parameter XXX

-    \(f_{1i}\) and \(E_{1}\) are given by clause 7.4.2.2 of [4, 38.212]

7.4.4.1.2     Generation of \(r_{\text{WUS}}(n)\) #

The block of complex-valued symbols \(r_{\text{WUS}}(0),\ldots,r_{\text{WUS}}\left( M_{\text{bit}}M_{\text{ZC}} - 1 \right)\) is defined by

\[r_{\text{WUS}}\left( {lN_{\text{sc}}^{\text{WUS}} + k} \right) = \frac{1}{\sqrt[{}]{N_{\text{sc}}^{\text{WUS}}}}\sum\limits_{i = 0}^{N_{\text{sc}}^{\text{WUS}} - 1}{{\overset{\sim}{r}}_{\text{WUS}}\left( {lN_{\text{sc}}^{\text{WUS}} + i} \right)e^{- j\frac{2\pi ik}{N_{\text{sc}}^{\text{WUS}}}}}\]

\[k = 0,1,\ldots,N_{\text{sc}}^{\text{WUS}} - 1\]

\[l = 0,1,\ldots,{M_{\text{bit}}/M_{\text{WUS}}} - 1\]

\[N_{\text{sc}}^{\text{WUS}} = 11N_{\text{sc}}^{\text{RB}}\]

where

\[{\overset{\sim}{r}}_{\text{WUS}}\left( {mM_{\text{ZC}} + n} \right) = b(m)r_{\text{ZC},\overset{\sim}{m}}(n)\]

\[\overset{\sim}{m} = \left\lfloor {m/2} \right\rfloor\]

\[m = 0,1,\ldots,M_{\text{bit}} - 1\]

\[n = 0,1,\ldots,M_{\text{ZC}} - 1\]

The quantity \(M_{\text{WUS}} \in \left\{ {1,2,4} \right\}\) is given by the higher-layer parameter LP-WUS_Mvalue_IDLE/INACTIVE or LP-WUS_Mvalue_CONNECTED.

The bit sequence \(b(0),\ldots,b\left( M_{\text{bit}} - 1 \right)\) and the number of bits \(M_{\text{bit}}\) corresponds to \(g_{00},g_{01},\ldots,g_{0{({G_{0} - 1})}}\) and \(G_{0}\), respectively, in clause 7.4.3 of [4, 38.212].

7.4.4.2     Mapping to physical resources #

The UE shall assume the block of complex-valued symbols \(r_{\text{WUS}}(0),\ldots,r_{\text{WUS}}\left( M_{\text{bit}}M_{\text{ZC}} - 1 \right)\) is scaled by a factor \(\beta_{\text{WUS}}\) and mapped to resource elements \(\left( {k,l} \right)_{p,\mu}\) used for WUS transmission in increasing order of first \(k\) and then \(l\).

7.4.5     Low-power synchronization signal #

7.4.5.1     Sequence generation #

7.4.5.1.1     Generation of \(r_{\text{OOK}}(n)\) #

The sequence \(r_{\text{OOK}}(0),\ldots,r_{\text{OOK}}\left( N_{\text{OOK}} - 1 \right)\) is defined by Tables 7.4.5.1.1-1 to 7.4.5.1.1-3 with the quantity \(M_{\text{LPSS}}\) given by the higher-layer parameter XXX.

 

Table 7.4.5.1.1-1: The sequence \(\begin{bmatrix} {\mathbf{r}_{\text{OOK}}(0)} & \cdots & {\mathbf{r}_{\text{OOK}}\left( \mathbf{N}_{\text{OOK}} - 1 \right)} \end{bmatrix}\) for \(\mathbf{M}_{\text{LPSS}} = 1\).

Configuration

Length 6

Length 8

0

[1 0 1 0 1 0]

[1 0 1 0 0 1 0 1]

1

[0 1 0 1 0 1]

[1 0 1 0 1 0 0 1]

2

[1 0 0 1 0 1]

[1 0 0 1 0 1 0 1]

3

[1 0 1 0 0 1]

[0 1 0 1 0 1 0 1]

 

Table 7.4.5.1.1-2: The sequence \(\begin{bmatrix} {\mathbf{r}_{\text{OOK}}(0)} & \cdots & {\mathbf{r}_{\text{OOK}}\left( \mathbf{N}_{\text{OOK}} - 1 \right)} \end{bmatrix}\) for \(\mathbf{M}_{\text{LPSS}} = 2\).

Configuration

Length 12

Length 16

0

[1 0 0 1 1 0 0 1 1 0 0 1]

[1 0 0 1 0 1 0 1 1 0 0 1 1 0 0 1]

1

[0 1 1 0 1 0 0 1 1 0 0 1]

[1 0 0 1 1 0 0 1 0 1 1 0 0 1 0 1]

2

[0 1 1 0 0 1 1 0 1 0 0 1]

[1 0 0 1 1 0 1 0 0 1 0 1 1 0 0 1]

3

[0 1 1 0 0 1 0 1 1 0 0 1]

[1 0 1 0 0 1 1 0 0 1 1 0 0 1 0 1]

 

Table 7.4.5.1.1-3: The sequence \(\begin{bmatrix} {\mathbf{r}_{\text{OOK}}(0)} & \cdots & {\mathbf{r}_{\text{OOK}}\left( \mathbf{N}_{\text{OOK}} - 1 \right)} \end{bmatrix}\) for \(\mathbf{M}_{\text{LPSS}} = 4\).

Configuration

Length 16

Length 32

0

[0 1 1 0 1 0 0 1 1 0 1 0 1 0 1 0]

[0 1 0 1 1 0 1 0 1 0 1 0 1 0 0 1 1 0 1 0 0 1 1 0 0 1 1 0 0 1 0 1]

1

[0 1 1 0 1 0 1 0 1 0 0 1 1 0 1 0]

[0 1 1 0 0 1 0 1 0 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 1 0 1 0 0 1 0 1]

2

[1 0 1 0 0 1 1 0 1 0 1 0 1 0 0 1]

[0 1 0 1 0 1 0 1 1 0 1 0 1 0 0 1 1 0 1 0 1 0 0 1 1 0 1 0 0 1 1 0]

3

[1 0 1 0 1 0 0 1 1 0 1 0 0 1 1 0]

[0 1 0 1 0 1 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 1 1 0 1 0 1 0 0 1 0 1]

 

7.4.5.1.2     Generation of \(r_{\text{ZC}}(n)\) #

If the quantity \(q\epsilon\left\{ {1,\ldots,N_{\text{ZC}} - 1} \right\}\) is configured by the higher-layer parameter XXX, the sequence \(r_{\text{ZC}}(n)\) is defined by

\[r_{\text{ZC}}(n) = x_{q}\left( {n\text{mod}N_{\text{ZC}}} \right)\]

\[x_{q}(i) = e^{- j\frac{\pi qi(i + 1)}{N_{\text{ZC}}}}\]

\[n = 0,1,\ldots,M_{\text{ZC}} - 1\]

where

-    \(N_{\text{ZC}}\) is the largest prime number such that \(N_{\text{ZC}} < M_{\text{ZC}}\)

-    \(M_{\text{ZC}} = {N_{\text{sc}}^{\text{WUS}}/M_{\text{LPSS}}}\)

7.4.5.1.3     Generation of \(r_{\text{LPSS}}(n)\) #

The block of complex-valued symbols \(r_{\text{LPSS}}(0),\ldots,r_{\text{LPSS}}\left( N_{\text{OOK}}M_{\text{ZC}} - 1 \right)\) is defined by

\[r_{\text{LPSS}}\left( {lN_{\text{sc}}^{\text{WUS}} + k} \right) = \frac{1}{\sqrt[{}]{N_{\text{sc}}^{\text{WUS}}}}\sum\limits_{i = 0}^{N_{\text{sc}}^{\text{WUS}} - 1}{{\overset{\sim}{r}}_{\text{LPSS}}\left( {lN_{\text{sc}}^{\text{WUS}} + i} \right)e^{- j\frac{2\pi ik}{N_{\text{sc}}^{\text{WUS}}}}}\]

\[k = 0,1,\ldots,N_{\text{sc}}^{\text{WUS}} - 1\]

\[l = 0,1,\ldots,{N_{\text{OOK}}/M_{\text{LPSS}}} - 1\]

\[N_{\text{sc}}^{\text{WUS}} = 11N_{\text{sc}}^{\text{RB}}\]

where

\[{\overset{\sim}{r}}_{\text{LPSS}}\left( {mM_{\text{ZC}} + n} \right) = r_{\text{OOK}}(m)r_{\text{ZC}}(n)\]

\[m = 0,1,\ldots,N_{\text{OOK}} - 1\]

\[n = 0,1,\ldots,M_{\text{ZC}} - 1\]

7.4.5.2     Mapping to physical resources #

The UE shall assume the block of complex-valued symbols \(r_{\text{LPSS}}(0),\ldots,r_{\text{LPSS}}\left( N_{\text{OOK}}M_{\text{ZC}} - 1 \right)\) is scaled by a factor \(\beta_{\text{LPSS}}\) and mapped to resource elements \(\left( {k,l} \right)_{p,\mu}\) used for LPSS transmission in increasing order of first \(k\) and then , then \(l\).

 

8     Sidelink #

8.1     Overview #

8.1.1     Overview of physical channels #

A sidelink physical channel corresponds to a set of resource elements carrying information originating from higher layers. The following sidelink physical channels are defined:

-    Physical Sidelink Shared Channel, PSSCH

-    Physical Sidelink Broadcast Channel, PSBCH

-    Physical Sidelink Control Channel, PSCCH

-    Physical Sidelink Feedback Channel, PSFCH

8.1.2     Overview of physical signals #

A sidelink physical signal corresponds to a set of resource elements used by the physical layer but does not carry information originating from higher layers.

The following sidelink physical signals are defined:

-    Demodulation reference signals, DM-RS

-    Channel-state information reference signal, CSI-RS

-    Phase-tracking reference signals, PT-RS

-    Sidelink primary synchronization signal, S-PSS

-    Sidelink secondary synchronization signal, S-SSS

-    Sidelink positioning reference signal, SL PRS

8 .2    Physical resources #

8.2.1     General #

In a shared SL PRS resource pool, the OFDM symbol immediately preceding the symbols which are configured for use by PSFCH if PSFCH is configured in this slot, and the last symbol configured for sidelink in a slot, serve as guard symbol(s). In a dedicated SL PRS resource pool, the last symbol configured for sidelink in a slot serves as a guard symbol. Otherwise, the OFDM symbol immediately following the last symbol used for PSSCH, PSFCH, or S-SSB serves as a guard symbol.

The first OFDM symbol of a PSSCH and its associated PSCCH is duplicated as described in clauses 8.3.1.5 and 8.3.2.3. The first OFDM symbol of a PSFCH is duplicated as described in clause 8.3.4.2.2.

The OFDM symbol immediately preceding an SL PRS resource in a dedicated SL PRS resource pool is generated as described in clause 8.4.1.6.3.

8.2.2     Numerologies #

Multiple OFDM numerologies are supported as given by Table 8.2.2-1 where \(\mu\) and the cyclic prefix for a sidelink bandwidth part are obtained from the higher-layer parameter sl-BWP.

Table 8.2.2-1: Supported transmission numerologies.

\[\mathbf{\mu}\]

\(\mathbf{\Delta}\mathbf{f} = 2^{\mathbf{\mu}} \bullet 15\) [kHz]

Cyclic prefix

0

15

Normal

1

30

Normal

2

60

Normal, Extended

3

120

Normal

 

8.2.3     Frame structure #

8.2.3.1     Frames and subframes #

The frame and subframe structure for sidelink transmission is defined in clause 4.3.1.

8.2.3.2     Slots #

The slot structure for sidelink transmission is defined in clause 4.3.2.

8.2.4     Antenna ports #

An antenna port is defined in clause 4.4.1.

The following antenna ports are defined for the sidelink:

-    Antenna ports starting with 1000 for PSSCH

-    Antenna ports starting with 2000 for PSCCH

-    Antenna ports starting with 3000 for CSI-RS

-    Antenna ports starting with 4000 for S-SS/PSBCH block

-    Antenna ports starting with 5000 for PSFCH

-    Antenna ports starting with 6000 for SL PRS

For DM-RS associated with a PSBCH, the channel over which a PSBCH symbol on one antenna port is conveyed can be inferred from the channel over which a DM-RS symbol on the same antenna port is conveyed only if the two symbols are within a S-SS/PSBCH block transmitted within the same slot, and with the same block index.

For DM-RS associated with a PSSCH, the channel over which a PSSCH symbol on one antenna port is conveyed can be inferred from the channel over which a DM-RS symbol on the same antenna port is conveyed only if the two symbols are within the same frequency resource as the scheduled PSSCH and in the same slot.

For DM-RS associated with a PSCCH, the channel over which a PSCCH symbol on one antenna port is conveyed can be inferred from the channel over which a DM-RS symbol on the same antenna port is conveyed only if the two symbols are within the same frequency resource as the transmitted PSCCH and in the same slot.

8.2.5     Resource grid #

The resource grid for sidelink transmission is defined in clause 4.4.2.

For sidelink, the carrier bandwidth \(N_{\text{grid}}^{\text{size},\mu}\) and the starting position \(N_{\text{grid}}^{\text{start},\mu}\) for subcarrier spacing configuration \(\mu\) are obtained from the higher-layer parameter sl-SCS-SpecificCarrierList.

For the sidelink, the higher-layer parameter sl-TxDirectCurrentLocation indicates the location of the transmitter DC subcarrier in the sidelink for each of the configured bandwidth parts. Values in the range 0 – 3299 represent the number of the DC subcarrier, the value 3300 indicates that the DC subcarrier is located outside the resource grid, and the value 3301 indicates that the position of the DC subcarrier in the sidelink is undetermined. The DC subcarrier location offset relative to the center of the indicated subcarrier is given by \(7.5 + 5N\text{kHz}\) if frequencyShift7p5khzSL is provided and by \(5N\text{kHz}\) otherwise, where \(N \in \left\{ {- 1,0,1} \right\}\) is given by the higher-layer parameter valueN.

8.2.6     Resource elements #

Resource elements are defined in clause 4.4.3.

8.2.7     Resource blocks #

Resource blocks are defined in clause 4.4.4.

Point A for sidelink transmission/reception is obtained from the higher-layer parameter sl-AbsoluteFrequencyPointA.

8.2.8     Bandwidth part #

Configuration of the single bandwidth part for sidelink transmission is described in clause 16 of [5, TS 38.213].

8.3     Physical channels #

8.3.1.1     Scrambling #

For the single codeword \(q = 0\), the block of bits \(b^{(q)}(0),\ldots,b^{(q)}\left( {M_{\text{bit}}^{(q)} - 1} \right)\), where \(M_{\text{bit}}^{(q)} = M_{\text{bit,SCI2}}^{(q)} + M_{\text{bit,data}}^{(q)}\) is the number of bits in codeword \(q\) transmitted on the physical channel as defined in [4, TS 38.212], shall be scrambled prior to modulation.

Scrambling shall be done according to the following pseudo code

set \(i = 0\)

set \(j = 0\)

while \(i < M_{\text{bit}}^{(q)}\)

if \(b^{(q)}(i) = x\)    // SCI placeholder bits

\({\overset{\sim}{b}}^{(q)}(i) = {\overset{\sim}{b}}^{(q)}\left( {i - 2} \right)\)

\(j = j + 1\)

else

    \({\overset{\sim}{b}}^{(q)}(i) = \left( {b^{(q)}(i) + c^{(q)}\left( i - {\overset{\sim}{M}}_{i,j}^{(q)} \right)} \right)\text{mod}2\)

end if

i = i + 1

end while

where the scrambling sequence \(c^{(q)}(i)\) is given by clause 5.2.1 and

-    for \(0 \leq i < M_{\text{bit,SCI2}}^{(q)}\)

-    \({\overset{\sim}{M}}_{i,j}^{(q)} = j\)

-    The scrambling sequence generator shall be initialized with

\[c_{\text{init}} = 2^{15}N_{\text{ID}} + 1010\]

    where \(N_{\text{ID}} = N_{\text{ID}}^{X}\text{mod}2^{16}\) and the quantity \(N_{\text{ID}}^{X}\) equals the decimal representation of the CRC on the PSCCH associated with the PSSCH according to \(N_{\text{ID}}^{X} = \sum_{i = 0}^{L - 1}p_{i} \bullet 2^{L - 1 - i}\) with \(p\) and \(L\) given by clause 8.3.2 in [4, TS 38.212].

-    for \(M_{\text{bit,SCI2}}^{(q)} \leq i < M_{\text{bit}}^{(q)}\)

-    \({\overset{\sim}{M}}_{i,j}^{(q)} = M_{\text{bit,SCI2}}^{(q)}\)

-    The scrambling sequence generator shall be initialized with

\[c_{\text{init}} = 2^{15}N_{\text{ID}} + 1010\]

    where \(N_{\text{ID}} = N_{\text{ID}}^{X}\text{mod}2^{16}\) and the quantity \(N_{\text{ID}}^{X}\) equals the decimal representation of the CRC on the PSCCH associated with the PSSCH according to \(N_{\text{ID}}^{X} = \sum_{i = 0}^{L - 1}p_{i} \bullet 2^{L - 1 - i}\) with \(p\) and \(L\) given by clause 8.3.2 in [4, TS 38.212].

8.3.1.2     Modulation #

For the single codeword \(q = 0\), the block of scrambled bits shall be modulated, resulting in a block of complex-valued modulation symbols \(d^{(q)}(0),\ldots,d^{(q)}\left( {M_{\text{symb}}^{(q)} - 1} \right)\) where \(M_{\text{symb}}^{(q)} = M_{\text{symb,1}}^{(q)} + M_{\text{symb,2}}^{(q)}\).

Modulation for \(0 \leq i < M_{\text{bit,SCI2}}^{(q)}\) shall be done as described in clause 5.1 using QPSK, where \(M_{\text{symb,1}}^{(q)} = {M_{\text{bit,SCI2}}^{(q)}/2}\).

Modulation for \(M_{\text{bit,SCI2}}^{(q)} \leq i < M_{\text{bit}}^{(q)}\) shall be done as described in clause 5.1 using one of the modulation schemes in Table 8.3.1.2-1 where \(M_{\text{symb,2}}^{(q)} = {M_{\text{bit,data}}^{(q)}/Q_{\text{m}}}\).

Table 8.3.1.2-1: Supported modulation schemes.

Modulation scheme

Modulation order \(\mathbf{Q}_{\mathbf{m}}\)

QPSK

2

16QAM

4

64QAM

6

256QAM

8

 

8.3.1.3     Layer mapping #

Layer mapping shall be done according to clause 7.3.1.3 with the number of layers \(\upsilon \in \left\{ 1,2 \right\}\), resulting in \(x(i) = \begin{bmatrix} {x^{(0)}(i)} & \ldots & {x^{(\upsilon - 1)}(i)} \end{bmatrix}^{\text{T}}\), \(i = 0,1,\ldots,M_{\text{symb}}^{\text{layer}} - 1\).

8.3.1.4     Precoding #

The block of vectors \(\begin{bmatrix} {x^{(0)}(i)} & \ldots & {x^{(\upsilon - 1)}(i)} \end{bmatrix}^{\text{T}}\) shall be precoded according to clasue 6.3.1.5 where the precoding matrix \(W\) equals the identity matrix and \(M_{\text{symb}}^{\text{ap}} = M_{\text{symb}}^{\text{layer}}\).

8.3.1.5     Mapping to virtual resource blocks #

For each of the antenna ports used for transmission of the PSSCH, the block of complex-valued symbols \(z^{(p)}(0),\ldots,z^{(p)}\left( M_{\text{symb}}^{\text{ap}} - 1 \right)\) shall be multiplied with the amplitude scaling factor \(\beta_{\text{DMRS}}^{\text{PSSCH}}\) in order to conform to the transmit power specified in [5, TS 38.213] and mapped to resource elements \((k',l)_{p,\mu}\) in the virtual resource blocks assigned for transmission, where \(k^{'} = 0\) is the first subcarrier in the lowest-numbered virtual resource block assigned for transmission.

The mapping operation shall be done in two steps:

-    first, the complex-valued symbols corresponding to the bit for the 2nd-stage SCI in increasing order of first the index \(k'\) over the assigned virtual resource blocks and then the index \(l\), starting from the first PSSCH symbol carrying an associated DM-RS and meeting all of the following criteria:

-    the corresponding resource elements in the corresponding physical resource blocks are not used for transmission of the associated DM-RS, PT-RS, or PSCCH;

-    secondly, the complex-valued modulation symbols not corresponding to the 2nd -stage SCI shall be in increasing order of first the index \(k'\) over the assigned virtual resource blocks, and then the index \(l\) with the starting position given by [6, TS 38.214] and meeting all of the following criteria:

-    the resource elements are not used for 2nd-stage SCI in the first step;

-    the resource elements are not in the \(L_{\text{SL-PRS}}\) symbols used for transmission of the associated SL PRS according to clause 8.2.4.1.1 of [6, TS 38.214];

-    the corresponding resource elements in the corresponding physical resource blocks are not used for transmission of the associated DM-RS, PT-RS, CSI-RS, or PSCCH.

The resource elements used for the PSSCH in the first OFDM symbol in the mapping operation above, including any DM-RS, PT-RS, or CSI-RS occurring in the first OFDM symbol, shall be duplicated in the OFDM symbol immediately preceding the first OFDM symbol in the mapping.

8.3.1.6     Mapping from virtual to physical resource blocks #

Virtual resource blocks shall be mapped to physical resource blocks according to non-interleaved mapping.

For non-interleaved VRB-to-PRB mapping, virtual resource block \(n\) is mapped to physical resource block \(n\).

8.3.2.1     Scrambling #

The block of bits \(b(0),\ldots,b\left( M_{\text{bit}} - 1 \right)\), where \(M_{\text{bit}}\) is the number of bits transmitted on the physical channel, shall be scrambled prior to modulation, resulting in a block of scrambled bits \(\overset{\sim}{b}(0),\ldots,\overset{\sim}{b}\left( M_{\text{bit}} - 1 \right)\) according to

\[\overset{\sim}{b}(i) = \left( {b(i) + c(i)} \right)\text{mod}2\]

where the scrambling sequence \(c(i)\) is given by clause 5.2.1. The scrambling sequence generator shall be initialized with

\[c_{\text{init}} = 1010\]

8.3.2.2     Modulation #

The block of scrambled bits \(\overset{\sim}{b}(0),\ldots,\overset{\sim}{b}\left( M_{\text{bit}} - 1 \right)\) shall be modulated as described in clause 5.1 using QPSK, resulting in a block of complex-valued modulation symbols \(d(0),\ldots,d\left( M_{\text{symb}} - 1 \right)\) where \(M_{\text{symb}} = {M_{\text{bit}}/2}\).

8.3.2.3     Mapping to physical resources #

The set of complex-valued modulation symbols \(d(0),\ldots,d\left( M_{\text{symb}} - 1 \right)\) shall be multiplied with the amplitude scaling factor \(\beta_{\text{DMRS}}^{\text{PSCCH}}\) in order to conform to the transmit power specified in [5, TS 38.213] and mapped in sequence starting with \(d(0)\) to resource elements \(\left( {k,l} \right)_{p,\mu}\) assigned for transmission according to clause 16.4 of [5, TS 38.213], and not used for the demodulation reference signals associated with PSCCH, in increasing order of first the index \(k\) over the assigned physical resources, and then the index \(l\) on antenna port\(p = 2000\).

The resource elements used for the PSCCH in the first OFDM symbol in the mapping operation above, including any DM-RS, PT-RS, or CSI-RS occurring in the first OFDM symbol, shall be duplicated in the immediately preceding OFDM symbol.

8.3.3.1     Scrambling #

The block of bits\(b(0),\ldots,b\left( M_{\text{bit}} - 1 \right)\), where \(M_{\text{bit}}\) is the number of bits transmitted on the physical sidelink broadcast channel, shall be scrambled prior to modulation, resulting in a block of scrambled bits \(\overset{\sim}{b}(0),\ldots,\overset{\sim}{b}\left( M_{\text{bit}} - 1 \right)\) according to

\[\overset{\sim}{b}(i) = \left( {b(i) + c(i)} \right)\text{mod}2\]

where the scrambling sequence \(c(i)\) is given by clause 5.2.1. The scrambling sequence generator shall be initialized with \(c_{\text{init}} = N_{\text{ID}}^{\text{SL}}\) at the start of each S-SS/PSBCH block.

8.3.3.2     Modulation #

The block of bits \(\overset{\sim}{b}(0),\ldots,\overset{\sim}{b}\left( M_{\text{bit}} - 1 \right)\) shall be QPSK modulated as described in clause 5.1.3, resulting in a block of complex-valued modulation symbols \(d_{\text{PSBCH}}(0),\ldots,d_{\text{PSBCH}}\left( M_{\text{symb}} - 1 \right)\) where \(M_{\text{symb}} = {M_{\text{bit}}/2}\).

8.3.3.3     Mapping to physical resources #

Mapping to physical resources is described in clause 8.4.3.

8.3.4.1     General #

8.3.4.2     PSFCH format 0 #

8.3.4.2.1     Sequence generation #

The sequence \(x(n)\) shall be generated according to

\[x(n) = r_{u,v}^{\alpha,\delta}(n)\]

\[n = 0,1,\ldots,N_{\text{sc}}^{\text{RB}} - 1\]

where \(r_{u,v}^{({\alpha,\delta})}(n)\) is given by clause 6.3.2.2 with the following exceptions:

-    \(m_{\text{cs}}\) is given by clause 16.3 of [5, TS 38.213];

-    \(m_{\text{0}}\) is given by clause 16.3 of [5, TS 38.213];

-    \(m_{\text{int}}\) is given by

-    \(m_{\text{int}} = {5n}_{\text{IRB}}^{\mu}\) if the higher-layer parameter sl-TransmissionStructureForPSFCH is configured and set to 'dedicatedInterlace' and where \(n_{\text{IRB}}^{\mu}\) is the resource block number within the interlace;

-    \(m_{\text{int}} = 0\) otherwise

-    \(l = 0\);

-    \(l'\) is the index of the OFDM symbol in the slot that corresponds to the second OFDM symbol of the PSFCH transmission in the slot given by [5, TS 38.213];

-    \(u = n_{\text{ID}}\text{mod}30\) and \(v = 0\) with \(n_{\text{ID}}\) given by the higher-layer parameter sl-PSFCH-HopID if configured; otherwise, \(u = 0\).

-    \(c_{\text{init}} = n_{\text{ID}}\) with \(n_{\text{ID}}\) given by the higher-layer parameter sl-PSFCH-HopID if configured; otherwise, \(c_{\text{init}} = 0\).

8.3.4.2.2     Mapping to physical resources #

The sequence \(x(n)\) shall be multiplied with the amplitude scaling factor \(\beta_{\text{PSFCH}}\) in order to conform to the transmit power specified in [5, TS 38.213] and mapped in sequence starting with \(x(0)\) to resource elements \(\left( {k,l} \right)_{p,\mu}\) assigned for transmission of the second PSFCH symbol according to clause 16.3 of [5, TS 38.213] in increasing order of the index \(k\) over the assigned physical resources on antenna port\(p = 5000\).

The resource elements used for the PSFCH in the OFDM symbol in the mapping operation above shall be duplicated in the immediately preceding OFDM symbol.

If the higher-layer parameter sl-TransmissionStructureForPSFCH is configured and set to 'dedicatedInterlace', the mapping operation shall be repeated for each resource block in the interlace and in the RB set over the assigned physical resource blocks according to clause 16.3 of [5, TS 38.213], with the resource-block dependent sequence generated according to clause 8.3.4.2.1.

If the higher-layer parameter sl-TransmissionStructureForPSFCH is configured and set to 'commonInterlace', the mapping operation shall be repeated for each resource block over the assigned physical resource blocks according to clause 16.3 of [5, TS 38.213], with the resource-block dependent sequence generated according to clause 8.3.4.2.1, where the cyclic shift \(\alpha\) on each resource block in the first interlace is up to UE implementation.

8.4     Physical signals #

8.4.1     Reference signals #

8.4.1.1     Demodulation reference signals for PSSCH #

8.4.1.1.1     Sequence generation #

The sequence \(r_{l}(m)\) shall be generated according to

\[r_{l}(m) = \frac{1}{\sqrt[{}]{2}}\left( {1 - 2c\left( {2m} \right)} \right) + j\frac{1}{\sqrt[{}]{2}}\left( {1 - 2c\left( {2m + 1} \right)} \right)\]

where the pseudo-random sequence \(c(m)\) is defined in clause 5.2.1. The pseudo-random sequence generator shall be initialized with

\[c_{\text{init}} = \left( {2^{17}\left( {N_{\text{symb}}^{\text{slot}}n_{\text{s,f}}^{\mu} + l + 1} \right)\left( {2N_{\text{ID}} + 1} \right) + 2N_{\text{ID}}} \right)\text{mod}2^{31}\]

where \(l\) is the OFDM symbol number within the slot, \(n_{\text{s,f}}^{\mu}\) is the slot number within a frame, and \(N_{\text{ID}} = N_{\text{ID}}^{X}\text{mod}2^{16}\) where the quantity \(N_{\text{ID}}^{X}\) equals the decimal representation of CRC on the PSCCH associated with the PSSCH according to \(N_{\text{ID}}^{X} = \sum_{i = 0}^{L - 1}p_{i} \bullet 2^{L - 1 - i}\) with \(p\) and \(L\) given by clause 7.3.2 in [4, TS 38.212].

8.4.1.1.2     Mapping to physical resources #

The sequence \(r(m)\) shall be mapped to the intermediate quantity \({\overset{\sim}{a}}_{k,l}^{({\overset{\sim}{p}}_{j},\mu)}\) according to clause 6.4.1.1.3 using configuration type 1 without transform precoding, and where \(w_{\text{f}}\left( {k'} \right)\), \(w_{\text{t}}\left( {l'} \right)\), and \(\Delta\) are given by Table 8.4.1.1.2-2, and \(r(m)\) is specified in clause 8.4.1.1.1.

The patterns used for the PSSCH DM-RS is indicated in the SCI as described in clause 8.3.1.1 of [4, TS 38.212].

The intermediate quantity \({\overset{\sim}{a}}_{k,l}^{({\overset{\sim}{p}}_{j},\mu)}\) shall be precoded, multiplied with the amplitude scaling factor \(\beta_{\text{DMRS}}^{\text{PSSCH}}\) specified in clause 8.3.1.5, and mapped to physical resources according to

\[\begin{bmatrix} a_{k,l}^{(p_{0},\mu)} \\ \vdots \\ a_{k,l}^{(p_{\rho - 1},\mu)} \end{bmatrix} = \beta_{\text{DMRS}}^{\text{PSSCH}}W\begin{bmatrix} {\overset{\sim}{a}}_{k,l}^{({\overset{\sim}{p}}_{0},\mu)} \\ \vdots \\ {\overset{\sim}{a}}_{k,l}^{({\overset{\sim}{p}}_{\upsilon - 1},\mu)} \end{bmatrix}\]

where

-    the precoding matrix \(W\) is given by clause 8.3.1.4,

-    the set of antenna ports \(\left\{ {p_{0},\ldots,p_{\rho - 1}} \right\}\) is given by clause 8.3.1.4, and

-    the set of antenna ports \(\left\{ {{\overset{\sim}{p}}_{0},\ldots,{\overset{\sim}{p}}_{\upsilon - 1}} \right\}\) is given by [6, TS 38.214];

and the following conditions are fulfilled:

-    the resource elements \({\overset{\sim}{a}}_{k,l}^{({\overset{\sim}{p}}_{j},\mu)}\) are within the common resource blocks allocated for PSSCH transmission.

The quantity \(k\) is defined relative to subcarrier 0 in common resource block 0 and the quantity \(l\) is defined relative to the start of the scheduled resources for transmission of PSSCH and the associated PSCCH, including the OFDM symbol duplicated as described in clauses 8.3.1.5 and 8.3.2.3.

The position(s) of the DM-RS symbols is given by \(\bar{l}\) according to Table 8.4.1.1.2-1 where the number of PSSCH DM-RS is indicated in the SCI, and \(l_{\text{d}}\) is the duration of the scheduled resources for transmission of PSSCH according to clause 8.1.2.1 of [6, TS 38.214] and the associated PSCCH, including the OFDM symbol duplicated as described in clauses 8.3.1.5 and 8.3.2.3.

Table 8.4.1.1.2-1: PSSCH DM-RS time-domain location.

\(\mathbf{l}_{\text{d}}\) in symbols

DM-RS position \(\bar{\mathbf{l}}\)

PSCCH duration 2 symbols

PSCCH duration 3 symbols

Number of PSSCH DM-RS

Number of PSSCH DM-RS

2

3

4

2

3

4

6

1, 5

 

 

1, 5

 

 

7

1, 5

 

 

1, 5

 

 

8

1, 5

 

 

1, 5

 

 

9

3, 8

1, 4, 7

 

4, 8

1, 4, 7

 

10

3, 8

1, 4, 7

 

4, 8

1, 4, 7

 

11

3, 10

1, 5, 9

1, 4, 7, 10

4, 10

1, 5, 9

1, 4, 7, 10

12

3, 10

1, 5, 9

1, 4, 7, 10

4, 10

1, 5, 9

1, 4, 7, 10

13

3, 10

1, 6, 11

1, 4, 7, 10

4, 10

1, 6, 11

1, 4, 7, 10

 

Table 8.4.1.1.2-2: Parameters for PSSCH DM-RS.

\[\mathbf{p}\]

CDM group \(\mathbf{\lambda}\)

\[\mathrm{\Delta}\]

\[\mathbf{w}_{\text{f}}\left( {\mathbf{k}\mathbf{'}} \right)\]

\[\mathbf{w}_{\text{t}}\left( {\mathbf{l}\mathbf{'}} \right)\]

 

 

 

\[\mathbf{k}^{\mathbf{'}} = 0\]

\[\mathbf{k}^{\mathbf{'}} = 1\]

\[\mathbf{l}^{\mathbf{'}} = 0\]

1000

0

0

+1

+1

+1

1001

0

0

+1

-1

+1

 

8.4.1.2     Phase-tracking reference signals for PSSCH #

8.4.1.2.1     Sequence generation #

The precoded sidelink phase-tracking reference signal for subcarrier \(k\) on layer \(j\) is given by

\[r^{({\overset{\sim}{p}}_{j})}(m) = \left\{ \begin{matrix} {r(m)} & {\text{if}j = j^{'}\text{or}j = j"} \\ 0 & \text{otherwise} \end{matrix} \right.\]

where

-    antenna ports \({\overset{\sim}{p}}_{j^{'}}\) or \(\left\{ {{\overset{\sim}{p}}_{j^{'}},{\overset{\sim}{p}}_{j^{''}}} \right\}\) associated with PT-RS transmission are given by clause 8.2.3 of [6, TS 38.214];

-    \(r(m)\) is given by clause 8.4.1.1.1 at the position of the first PSSCH symbol carrying an associated DM-RS.

8.4.1.2.2     Mapping to physical resources #

The UE shall transmit phase-tracking reference signals only in the resource blocks used for the PSSCH, and only if the procedure in [6, TS 38.214] indicates that phase-tracking reference signals are being used.

The PSSCH PT-RS shall be mapped to resource elements according to

    \(\begin{bmatrix} a_{k,l}^{({p_{o},\mu})} \\ \vdots \\ a_{k,l}^{({p_{\rho - 1},\mu})} \end{bmatrix} = \beta_{\text{DMRS}}^{\text{PSSCH}}W\begin{bmatrix} {r^{{(\overset{\sim}{p}}_{0})}(2n + k')} \\ \vdots \\ {r^{{(\overset{\sim}{p}}_{\upsilon - 1})}(2n + k')} \end{bmatrix}\)

\[k = 4n + 2k^{'} + \Delta\]

when all the following conditions are fulfilled

-    \(l\) is within the OFDM symbols allocated for the PSSCH transmission;

-    resource element \(\left( {k,l} \right)\) is not used for PSCCH, nor DM-RS associated with PSSCH;

-    \(k'\) and \(\Delta\) correspond to \({\overset{\sim}{p}}_{0},\ldots,{\overset{\sim}{p}}_{\upsilon - 1}\)

The precoding matrix \(W\) is given by clause 8.3.1.4.

The set of time indices \(l\) defined relative to the start of the PSSCH allocation is defined by

1. set \(i = 0\)and \(l_{\text{ref}} = 0\)

2. if any symbol in the interval \(\max\left( {l_{\text{ref}} + \left( {i - 1} \right)L_{\text{PT-RS}} + 1,l_{\text{ref}}} \right),\ldots,l_{\text{ref}} + iL_{\text{PT-RS}}\) overlaps with a symbol used for DM-RS according to clause 8.4.1.1.2

-    set \(i = 1\)

-    set \(l_{\text{ref}}\) to the symbol index of the DM-RS symbol

-    repeat from step 2 as long as \(l_{\text{ref}} + iL_{\text{PT-RS}}\) is inside the PSSCH allocation

3. add \(l_{\text{ref}} + iL_{\text{PT-RS}}\) to the set of time indices for PT-RS

4. increment \(i\) by one

5. repeat from step 2 above as long as \(l_{\text{ref}} + iL_{\text{PT-RS}}\) is inside the PSSCH allocation

where \(L_{\text{PT-RS}} \in \left\{ {1,2,4} \right\}\) is given by clause 8.4.3 of [6, TS 38.214].

For the purpose of PT-RS mapping, the resource blocks allocated for PSSCH transmission are numbered from 0 to \(N_{\text{RB}} - 1\) from the lowest scheduled resource block to the highest. The corresponding subcarriers in this set of resource blocks are numbered in increasing order starting from the lowest frequency from 0 to \(N_{\text{sc}}^{\text{RB}}N_{\text{RB}} - 1\). The subcarriers to which the PT-RS shall be mapped are given by

k=krefRE+iKPT-RS+krefRBNscRBkrefRB=NID mod KPT-RSif NRB mod KPT-RS=0NID mod NRB mod KPT-RSotherwise

where

-    \(i = 0,1,2,\ldots\)

-    \(k_{\text{ref}}^{\text{RE}}\) is given by Table 8.4.1.2.2-1 for the DM-RS port associated with the PT-RS port according to clause 8.2.3 in [6, TS 38.214].

-    \(N_{\text{RB}}\) is the number of resource blocks scheduled;

-    \(K_{\text{PT-RS}} \in \left\{ 2,4 \right\}\) is given by [6, TS 38.214];

-    \(N_{\text{ID}} = N_{\text{ID}}^{X}\text{mod}2^{16}\) where the quantity \(N_{\text{ID}}^{X}\) equals the decimal representation of CRC on the PSCCH associated with the PSSCH according to \(N_{\text{ID}}^{X} = \sum_{i = 0}^{L - 1}p_{i} \bullet 2^{L - 1 - i}\) with \(p\) and \(L\) given by clause 7.3.2 in [4, TS 38.212].

PSSCH PT-RS shall not be mapped to resource elements containing PSCCH or PSCCH DMRS by puncturing PSSCH PT-RS.

A UE is not expected to receive sidelink CSI-RS and PSSCH PT-RS on the same resource elements.

 

Table 8.4.1.2.2-1: The parameter \(\mathbf{k}_{\text{ref}}^{\text{RE}}\) .

DM-RS antenna port

\[\mathbf{k}_{\text{ref}}^{\text{RE}}\]

\[\overset{\sim}{\mathbf{p}}\]

resourceElementOffset

 

offset00

offset01

offset10

offset11

0

0

2

6

8

1

2

4

8

10

 

8.4.1.3     Demodulation reference signals for PSCCH #

8.4.1.3.1     Sequence generation #

The sequence \(r_{l}(m)\) shall be generated according to

\[r_{l}(m) = \frac{1}{\sqrt[{}]{2}}\left( {1 - 2c\left( {2m} \right)} \right) + j\frac{1}{\sqrt[{}]{2}}\left( {1 - 2c\left( {2m + 1} \right)} \right)\]

where the pseudo-random sequence \(c(m)\) is defined in clause 5.2.1. The pseudo-random sequence generator shall be initialized with

\[c_{\text{init}} = \left( {2^{17}\left( {N_{\text{symb}}^{\text{slot}}n_{s,f}^{\mu} + l + 1} \right)\left( {2N_{\text{ID}} + 1} \right) + {2N}_{\text{ID}}} \right)\text{mod}2^{31}\]

where

-    \(l\) is the OFDM symbol number within the slot,

-    \(n_{s,f}^{\mu}\) is the slot number within a frame, and

-    \(N_{ID} \in \left\{ 0,1,\ldots,65535 \right\}\) is given by the higher-layer parameter sl-DMRS-ScrambleID, or is given by the higher-layer parameter sl-DMRS-ScrambleID-DedicatedSL-PRS-RP when the resource pool is a dedicated SL PRS resource pool.

8.4.1.3.2     Mapping to physical resources #

The sequence \(r_{l}(m)\) shall be multiplied with the amplitude scaling factor \(\beta_{\text{DMRS}}^{\text{PSCCH}}\) in order to conform to the transmit power specified in [5, 38.213] and mapped in sequence starting with \(r_{l}(0)\) to resource elements \(\left( {k,l} \right)_{p,\mu}\) in a slot on antenna port \(p = 2000\) according to

\[\begin{matrix} {a_{k,l}^{(p,\mu)} = \beta_{\text{DMRS}}^{\text{PSCCH}}{w_{\text{f},i}(k')r}_{l}\left( {3n + k'} \right)} \\ {k = nN_{\text{sc}}^{\text{RB}} + 4k^{'} + 1} \\ {k^{'} = 0,1,2} \\ {n = 0,1,\ldots} \end{matrix}\]

where the following conditions are fulfilled

-    they are within the resource elements constituting the PSCCH

The quantity \(w_{\text{f},i}(k')\) is given by Table 8.4.1.3.2-1 and \(i \in \left\{ {0,1,2} \right\}\) shall be randomly selected="selected" by the UE.

The reference point for \(k\) is subcarrier 0 in common resource block 0.

The quantity \(l\) is the OFDM symbol number within the slot.

Table 8.4.1.3.2-1: The quantity \(\mathbf{w}_{\text{f},\mathbf{i}}\left( \mathbf{k}\mathbf{'} \right)\).

\[\mathbf{k}\mathbf{'}\]

\[\mathbf{w}_{\mathbf{f},\mathbf{i}}\left( \mathbf{k}\mathbf{'} \right)\]

\[\mathbf{i} = 0\]

\[\mathbf{i} = 1\]

\[\mathbf{i} = 2\]

0

1

1

1

1

1

\[e^{j2/3\pi}\]

\[e^{- j2/3\pi}\]

2

1

\[e^{- j2/3\pi}\]

\[e^{j2/3\pi}\]

 

8.4.1.4     Demodulation reference signals for PSBCH #

8.4.1.4.1     Sequence generation #

The reference-signal sequence \(r(m)\) for an S-SS/PSBCH block is defined by

\[r(m) = \frac{1}{\sqrt[{}]{2}}\left( {1 - 2c\left( {2m} \right)} \right) + j\frac{1}{\sqrt[{}]{2}}\left( {1 - 2c\left( {2m + 1} \right)} \right)\]

where \(c(n)\) is given by clause 5.2. The scrambling sequence generator shall be initialized at the start of each S-SS/PSBCH block occasion with

\[c_{\text{init}} = N_{\text{ID}}^{\text{SL}}\]

8.4.1.4.2     Mapping to physical resources #

Mapping to physical resources is described in clause 8.4.3.

8.4.1.5     CSI reference signals #

8.4.1.5.1     General #
8.4.1.5.2     Sequence generation #

The sequence \(r(m)\) shall be generated according to

\[r(m) = \frac{1}{\sqrt[{}]{2}}\left( {1 - 2c\left( {2m} \right)} \right) + j\frac{1}{\sqrt[{}]{2}}\left( {1 - 2c\left( {2m + 1} \right)} \right)\]

where the pseudo-random sequence \(c(i)\) is defined in clause 5.2.1. The pseudo-random sequence generator shall be initialised with

\[c_{\text{init}} = \left( {2^{10}\left( {N_{\text{symb}}^{\text{slot}}n_{\text{s,f}}^{\mu} + l + 1} \right)\left( {2n_{\text{ID}} + 1} \right) + n_{\text{ID}}} \right)\text{mod}2^{31}\]

at the start of each OFDM symbol where \(n_{\text{s,f}}^{\mu}\) is the slot number within a radio frame, \(l\) is the OFDM symbol number within a slot, and \(n_{\text{ID}} = N_{\text{ID}}^{X}\text{mod}2^{10}\) where the quantity \(N_{\text{ID}}^{X}\) equals the decimal representation of CRC for the sidelink control information mapped to the PSCCH associated with the CSI-RS according to \(N_{\text{ID}}^{X} = \sum_{i = 0}^{L - 1}p_{i} \bullet 2^{L - 1 - i}\) with \(p\) and \(L\) given by clause 7.3.2 in [4, TS 38.212].

8.4.1.5.3     Mapping to physical resources #

Mapping to resource elements shall be done according to clause 7.4.1.5.3 with the following exceptions:

-    only 1 and 2 antenna ports are supported, \(X \in \left\{ 1,2 \right\}\);

-    only density \(\rho = 1\) is supported;

-    zero-power CSI-RS is not supported;

-    the quantity \(\beta_{\text{CSIRS}}\) is an amplitude scaling factor to conform with the transmit power specified in clause 8.2.1 of [6, TS 38.214].

8.4.1.6     Positioning reference signals #

8.4.1.6.1     General #

A SL PRS resource refers to a time-frequency resource within a slot, used for SL PRS transmission.

8.4.1.6.2     Sequence generation #

The sequence \(r(m)\) is defined by

\[r(m) = \frac{1}{\sqrt[{}]{2}}\left( {1 - 2c\left( {2m} \right)} \right) + j\frac{1}{\sqrt[{}]{2}}\left( {1 - 2c\left( {2m + 1} \right)} \right)\]

where the pseudo-random sequence \(c(i)\) is defined in clause 5.2.1. The pseudo-random sequence generator shall be initialised with

\[c_{\text{init}} = \left( {2^{22}\left\lfloor \frac{n_{\text{ID,seq}}^{\text{SL-PRS}}}{1024} \right\rfloor + 2^{10}\left( {N_{\text{symb}}^{\text{slot}}n_{\text{s,f}}^{\mu} + l + 1} \right)\left( {2\left( {n_{\text{ID,seq}}^{\text{SL-PRS}}\text{mod}1024} \right) + 1} \right) + \left( {n_{\text{ID,seq}}^{\text{SL-PRS}}\text{mod}1024} \right)} \right)\text{mod}2^{31}\]

where

-    \(n_{\text{s,f}}^{\mu}\) is the slot number within the radio frame

-    \(l\) is the OFDM symbol number within the slot to which the sequence is mapped

-    \(n_{\text{ID,seq}}^{\text{SL-}\text{PRS}} \in \left\{ {0,1,\ldots,4095} \right\}\) is the sidelink PRS sequence ID, which, if not provided by higher layers, is obtained from the decimal representation of the CRC for the sidelink control information mapped to the PSCCH associated with the SL PRS according to \(n_{\text{ID,seq}}^{\text{SL-}\text{PRS}} = \left( {\sum_{i = 0}^{L - 1}p_{i} \bullet 2^{L - 1 - i}} \right)\text{mod}2^{12}\) with \(p\) and \(L\) given by clause 7.3.2 in [4, TS 38.212].

8.4.1.6.3     Mapping to physical resources #

The sequence shall be multiplied with the amplitude scaling factor \(\beta_{\text{SL-PRS}}\) in order to conform to the transmit power specified in [5, TS 38.213] and mapped to resources elements \(\left( {k,l} \right)_{p,\mu}\) according to

\[\begin{matrix} {a_{k,l}^{({p,\mu})} = \beta_{\text{SL-PRS}}r(m)} \\ {m = 0,1,\ldots} \\ {k = mK_{\text{comb}}^{\text{SL-PRS}} + \left( {\left( {k_{\text{offset}}^{\text{SL-PRS}} + k'} \right)\text{mod}K_{\text{comb}}^{\text{SL-PRS}}} \right)} \\ {l = l_{\text{start}}^{\text{SL-PRS}},l_{\text{start}}^{\text{SL-PRS}} + 1,\ldots,l_{\text{start}}^{\text{SL-PRS}} + L_{\text{SL-PRS}} - 1} \end{matrix}\]

when the following conditions are fulfilled:

-    the resource element \(\left( {k,l} \right)_{p,\mu}\) is within the common resource blocks occupied by the SL PRS resource

and where

-    the comb size \(K_{\text{comb}}^{\text{SL-}\text{PRS}}\) is provided by the higher layer parameter sl-PRS-CombSizeN-AndReOffset for a shared SL PRS resource pool and by the higher layer parameter sl-CombSize for a dedicated SL PRS resource pool

-    the resource-element offset \(k_{\text{offset}}^{\text{SL-}\text{PRS}} \in \left\{ {0,1,\ldots,K_{\text{comb}}^{\text{SL-}\text{PRS}} - 1} \right\}\)

-    the frequency offset \(k'\) is given by Table 8.4.1.6.3-1

-    the starting symbol \(l_{\text{start}}^{\text{SL-PRS}}\) is provided by the higher-layer parameter sl-PRS-starting-symbol for a dedicated SL PRS resource pool, or is determined such that the symbols {\(l_{\text{start}}^{\text{SL-PRS}},l_{\text{start}}^{\text{SL-PRS}} + 1,\ldots,l_{\text{start}}^{\text{SL-PRS}} + L_{SL - \text{PRS}} - 1\)} are mapped to the last consecutive \(L_{SL - \text{PRS}}\) symbols in the slot that can be used for SL PRS for a shared SL PRS resource pool as described in clause 8.2.4.1.1 in [6, TS38.214]

-    the number of symbols \(L_{\text{SL-}\text{PRS}}\) is provided by the higher-layer parameter mNumberOfSymbols for a shared resource pool and by the higher layer parameter sl-NumberOfSymbols for a dedicated resource pool and limited to combinations \(\left\{ {L_{\text{SL-}\text{PRS}},K_{\text{comb}}^{\text{SL-PRS}}} \right\}\) fulfilling

-    in a dedicated SL PRS resource pool: {1, 2}, {2, 2}, {2, 4}, {4, 4}, {6, 6}, and combinations with \(K_{\text{comb}}^{\text{SL-PRS}} \in \left\{ {2,4,6} \right\}\) and \(L_{\text{SL-PRS}} \in \left\{ {3,4,\ldots,9} \right\}\) where \(L_{\text{SL-}\text{PRS}} > K_{\text{comb}}^{\text{SL-PRS}}\)

-    in a shared SL PRS resource pool: {1, 1}, {1, 2}, {2, 1}, {2, 2}, {2, 4}, {4, 1}, {4, 2}, {4, 4}

-    the antenna port \(p = 6000\)

The reference point for \(k\) is subcarrier 0 in common resource block 0.

For transmission of an SL PRS in a dedicated SL PRS resource pool, the content of the OFDM symbol immediately preceding the SL PRS resource shall be generated based on 8.4.1.6.2 and mapped to resource elements with

-    the time-domain index \(l = l_{\text{start}}^{\text{SL-}\text{PRS}} - 1\)

-    the set of frequency-domain indices \(k\) shall be identical to those of the last OFDM symbol in the SL PRS resource

-    the amplitude scaling factor shall be same as the amplitude scaling factor \(\beta_{\text{SL-PRS}}\) of the SL PRS resource.

 

Table 8.4.1.6.3-1: The frequency offset \(\mathbf{k}\mathbf{'}\) as a function of \(\mathbf{l} - \mathbf{l}_{\text{start}}^{\text{SL-PRS}}\).

\[\mathbf{K}_{\text{comb}}^{\text{SL-}\text{PRS}}\]

Symbol number within the sidelink PRS resource \(\mathbf{l} - \mathbf{l}_{\text{start}}^{\text{SL-}\text{PRS}}\)

0

1

2

3

4

5

6

7

8

1

0

0

0

0

0

0

0

0

0

2

0

1

0

1

0

1

0

1

0

4

0

2

1

3

0

2

1

3

0

6

0

3

1

4

2

5

0

3

1

 

8.4.2     Synchronization signals #

There are 672 unique physical-layer sidelink synchronization identities given by

    \(N_{\text{ID}}^{\text{SL}} = N_{\text{ID,1}}^{\text{SL}} + 336N_{\text{ID,2}}^{\text{SL}}\)

where \(N_{\text{ID,1}}^{\text{SL}} \in \left\{ {0,1,\ldots,335} \right\}\) and \(N_{\text{ID,2}}^{\text{SL}} \in \left\{ 0,1 \right\}\). The sidelink synchronization identities are divided into two sets, id_net consisting of \(N_{\text{ID}}^{\text{SL}} = 0,1,\ldots,335\) and id_oon consisting of \(N_{\text{ID}}^{\text{SL}} = 336,337,\ldots,671\).

8.4.2.2.1     Sequence generation #

The sequence \(d_{\text{S-PSS}}(n)\) for the sidelink primary synchronization signal is defined by

\[\begin{matrix} {d_{\text{S-PSS}}(n) = 1 - 2x(m)} \\ {m = \left( {n + 22 + 43N_{I\text{D,2}}^{\text{SL}}} \right)\text{mod}127} \\ {0 \leq n < 127} \end{matrix}\]

where

\[x\left( {i + 7} \right) = \left( {x\left( {i + 4} \right) + x(i)} \right)\text{mod}2\]

and

\[\begin{bmatrix} {x(6)} & {x(5)} & {x(4)} & {x(3)} & {x(2)} & {x(1)} & {x(0)} \end{bmatrix} = \begin{bmatrix} 1 & 1 & 1 & 0 & 1 & 1 & 0 \end{bmatrix}\]

8.4.2.2.2     Mapping to physical resources #

Mapping to physical resources is described in clause 8.4.3.

8.4.2.3.1     Sequence generation #

The sequence \(d_{\text{S-SSS}}(n)\) for the sidelink secondary synchronization signal is defined by

\[\begin{matrix} {d_{\text{S-SSS}}(n) = \left\lbrack {1 - 2x_{0}\left( {\left( {n + m_{0}} \right)\text{mod}127} \right)} \right\rbrack\left\lbrack {1 - 2x_{1}\left( {\left( {n + m_{1}} \right)\text{mod}127} \right)} \right\rbrack} \\ {m_{0} = 15\left\lfloor \frac{N_{\text{ID},1}^{\text{SL}}}{112} \right\rfloor + 5N_{\text{ID},2}^{\text{SL}}} \\ {m_{1} = N_{\text{ID},1}^{\text{SL}}\text{mod}112} \\ {0 \leq n < 127} \end{matrix}\]

where

\[\begin{matrix} {x_{0}\left( {i + 7} \right) = \left( {x_{0}\left( {i + 4} \right) + x_{0}(i)} \right)\text{mod}2} \\ {x_{1}\left( {i + 7} \right) = \left( {x_{1}\left( {i + 1} \right) + x_{1}(i)} \right)\text{mod}2} \end{matrix}\]

and

x06x05x04x03x02x01x00=0000001x16x15x14x13x12x11x10=0000001

8.4.2.3.2     Mapping to physical resources #

Mapping to physical resources is described in clause 8.4.3.

8.4.3     S-SS/PSBCH block #

8.4.3.1     Time-frequency structure of an S-SS/PSBCH block #

In the time domain, an S-SS/PSBCH block consists of \(N_{\text{symb}}^{\text{S-SSB}}\) OFDM symbols, numbered in increasing order from 0 to \(N_{\text{symb}}^{\text{S-SSB}} - 1\) within the S-SS/PSBCH block, where S-PSS, S-SSS, and PSBCH with associated DM-RS are mapped to symbols as given by Table 8.4.3.1-1. The number of OFDM symbols in an S-SS/PSBCH block \(N_{\text{symb}}^{\text{S-SSB}} = 13\) for normal cyclic prefix and \(N_{\text{symb}}^{\text{S-SSB}} = 11\) for extended cyclic prefix. The first OFDM symbol in an S-SS/PSBCH block is the first OFDM symbol in the slot.

In the frequency domain, an S-SS/PSBCH block consists of 132 contiguous subcarriers with the subcarriers numbered in increasing order from 0 to 131 within the sidelink S-SS/PSBCH block. The quantities \(k\) and \(l\) represent the frequency and time indices, respectively, within one sidelink S-SS/PSBCH block.

For an S-SS/PSBCH block, the UE shall use

-    antenna port 4000 for transmission of S-PSS, S-SSS, PSBCH and DM-RS for PSBCH;

-    the same cyclic prefix length and subcarrier spacing for the S-PSS, S-SSS, PSBCH and DM-RS for PSBCH,

 

Table 8.4.3.1-1: Resources within an S-SS/PSBCH block for S-PSS, S-SSS, PSBCH, and DM-RS.

Channel or signal

OFDM symbol number \(\mathbf{l}\)relative to the start of an S-SS/PSBCH block<br>

Subcarrier number \(\mathbf{k}\)relative to the start of an S-SS/PSBCH block<br>

S-PSS

1, 2

2, 3, …, 127, 128

S-SSS

3, 4

2, 3, …, 127, 128

Set to zero

1, 2, 3, 4

0, 1, 129, 130, 131

PSBCH

0, 5, 6, …, \(N_{\text{symb}}^{\text{S-SSB}} - 1\)

0, 1,…, 131

DM-RS for PSBCH

0, 5, 6, …, \(N_{\text{symb}}^{\text{S-SSB}} - 1\)

0, 4, 8, …., 128

 

8.4.3.1.1     Mapping of S-PSS within an S-SS/PSBCH block #

The sequence of symbols \(d_{\text{S-PSS}}(0),\ldots,d_{\text{S-PSS}}(126)\) constituting the sidelink primary synchronization signal in one OFDM symbol shall be scaled by a factor \(\beta_{\text{S-PSS}}\) to conform to the S-PSS power allocation specified in [5, TS 38.213] and mapped to resource elements \((k,l)_{p,\mu}\) in increasing order of \(k\) in each of the symbols \(l\), where \(k\) and \(l\) are given by Table 8.4.3.1-1 and represent the frequency and time indices, respectively, within one S-SS/PSBCH block.

8.4.3.1.2     Mapping of S-SSS within an S-SS/PSBCH block #

The sequence of symbols \(d_{\text{S-SSS}}(0),\ldots,d_{\text{S-SSS}}(126)\) constituting the sidelink secondary synchronization signal in one OFDM symbol shall be scaled by a factor \(\beta_{\text{S-SSS}}\) to conform to the S-SSS power allocation specified in [5, TS 38.213] and mapped to resource elements \((k,l)_{p,\mu}\) in increasing order of \(k\) in each of the symbols \(l\), where \(k\) and \(l\) are given by Table 8.4.3.1-1 and represent the frequency and time indices, respectively, within one S-SS/PSBCH block.

8.4.3.1.3     Mapping of PSBCH and DM-RS within an S-SS/PSBCH block #

The sequence of complex-valued symbols \(d_{\text{PSBCH}}(0),\ldots,d_{\text{PSBCH}}\left( {M_{\text{symb}} - 1} \right)\) constituting the physical sidelink broadcast channel shall be scaled by a factor \(\beta_{\text{DMRS}}^{\text{PSBCH}}\) to conform to the PSBCH power allocation specified in [5, TS 38.213] and mapped in sequence starting with \(d_{\text{PSBCH}}(0)\) to resource elements \((k,l)_{p,\mu}\) which meet all the following criteria:

-    they are not used for PSBCH demodulation reference signals

The mapping to resource elements \((k,l)_{p,\mu}\) not reserved for PSBCH DM-RS shall be in increasing order of first the index \(k\) and then the index\(l\), where \(k\) and \(l\) represent the frequency and time indices, respectively, within one S-SS/PSBCH block and are given by Table 8.4.3.1-1.

The sequence of complex-valued symbols \(r(0),\ldots,r\left( {33\left( {N_{\text{symb}}^{\text{S-SSB}} - 4} \right) - 1} \right)\) constituting the demodulation reference signals for the S-SS/PSBCH block shall be scaled by a factor of \(\beta_{\text{DMRS}}^{\text{PSBCH}}\) to conform to the PSBCH power allocation specified in [5, TS 38.213] and mapped to resource elements \((k,l)_{p,\mu}\) in increasing order of first \(k\) and then \(l\) where \(k\) and \(l\) are given by Table 8.4.3.1-1 and represent the frequency and time indices, respectively, within one S-SS/PSBCH block.

8.4.3.2     Time location of an S-SS/PSBCH block #

The locations in the time domain where a UE shall monitor for a possible S-SS/PSBCH block are described in clause 16.1 of [5, TS 38.213].

8.5     Timing #

Transmission of a sidelink radio frame number \(i\) from the UE shall start \(\left( N_{TA,\text{SL}} + N_{TA,\text{offset}} \right) \bullet T_{c}\) seconds before the start of the corresponding timing reference frame at the UE. The UE is not required to receive sidelink or downlink transmissions earlier than the value of \(N_{TA,\text{offset}}\), which is given in [12, TS 38.133], after the end of a sidelink transmission.

For sidelink transmissions:

If the UE has a serving cell fulfilling the S criterion according to clause 8.2 of [13, TS 38.304]

-    The timing of reference radio frame \(i\) equals that of downlink radio frame \(i\) in the cell with the same uplink carrier frequency as the sidelink and

-    \(N_{TA,\text{offset}}\) is given by clause 4.3.1 of [TS 38.211],

Otherwise

-    The timing of reference radio frame i and \(N_{TA,\text{offset}}\) value are given by clause 12.2.2, 12.2.3, 12.2.4 or 12.2.5 of [12, TS 38.133].

Image

Figure 8.5-1: Sidelink timing relation

The quantity \(N_{TA,\text{SL}}\) equals to 0.

 

<br>Annex A (informative): Change history<br> #

 

Change history

Date

Meeting

TDoc

CR

Rev

Cat

Subject/Comment

New version

2017-04

RAN1#89

R1-1708219

 

 

 

Draft skeleton

0.0.0

2017-05

AH_1706

R1-1711366

 

 

 

Inclusion of agreements up to and including RAN1#89

0.0.1

2017-06

AH_1706

R1-1711886

 

 

 

Updated editor's version

0.0.2

2017-06

AH_1706

R1-1712004

 

 

 

Clean version further to RAN1's endorsement

0.1.0

2017-07

AH_1706

R1-1712011

 

 

 

Inclusion of agreements up to and including RAN1 NR AdHoc #2

0.1.1

2017-08

AH_1706

R1-1712950

 

 

 

Updated editor's version

0.1.2

2017-08

RAN1#90

R1-1713296

 

 

 

Updated editor's version

0.1.3

2017-08

RAN1#90

R1-1714656

 

 

 

Endorsed by RAN1#90

0.2.0

2017-08

RAN1#90

R1-1715321

 

 

 

Inclusion of agreements from RAN1#90

0.2.1

2017-09

RAN1#90

R1-1715329

 

 

 

Updated editor's version

0.2.2

2017-09

RAN#77

RP-171994

 

 

 

For information to plenary

1.0.0

2017-09

AH_1709

R1-1716927

 

 

 

Inclusion of agreements from AdHoc#3

1.0.1

2017-09

AH_1709

R1-1718318

 

 

 

Updated editor's version

1.0.2

2017-10

RAN1#90b

R1-1719105

 

 

 

Endorsed by RAN1#90bis

1.1.0

2017-10

RAN1#90b

R1-1719224

 

 

 

Inclusion of agreements from RAN1#90bis

1.1.1

2017-11

RAN1#90b

R1-1719685

 

 

 

Updated editor's version

1.1.2

2017-11

RAN1#90b

R1-1720850

 

 

 

Updated editor's version

1.1.3

2017-11

RAN1#90b

R1-1721048

 

 

 

Endorsed by RAN1#90bis

1.2.0

2017-12

RAN1#91

R1-17xxxxx

 

 

 

Inclusion of agreements from RAN1#91

1.2.1

2017-12

RAN1#91

R1-1721341

 

 

 

Endorsed by RAN1#91

1.3.0

2017-12

RAN#78

RP-172284

 

 

 

For approval by plenary

2.0.0

2017-12

RAN#78

 

 

 

 

Approved by plenary – Rel-15 spec under change control

15.0.0

2018-03

RAN#79

RP-180200

0001

-

F

CR capturing the Jan18 ad-hoc and RAN1#92 meeting agreements

15.1.0

2018-06

RAN#80

RP-181172

0002

1

F

CR to 38.211 capturing the RAN1#92bis and RAN1#93 meeting agreements

15.2.0

2018-09

RAN#81

RP-181789

0003

-

F

Corrections according to agreements from RAN1#94

15.3.0

2018-12

RAN#82

RP-182523

0004

1

F

Combined CR of all essential corrections to 38.211 from RAN1#94bis and RAN1#95

15.4.0

2019-03

RAN#83

RP-190447

0005

-

F

CR for PUCCH Format 1

15.5.0

2019-03

RAN#83

RP-190447

0006

-

F

CR on PDSCH mapping to virtual resource blocks

15.5.0

2019-03

RAN#83

RP-190447

0007

2

F

Alignment of terminology across specifications

15.5.0

2019-03

RAN#83

RP-190447

0008

-

F

Correction on physical resource mapping for PUSCH with configured grant

15.5.0

2019-03

RAN#83

RP-190773

0009

1

F

Correction to frequency-domain starting position for SRS resource mapping

15.5.0

2019-06

RAN#84

RP-191281

0010

-

F

CR on PUCCH format 1

15.6.0

2019-06

RAN#84

RP-191281

0011

-

F

Correction on reference name of UE capability of additional DMRS for co-existence with LTE CRS

15.6.0

2019-06

RAN#84

RP-191281

0012

-

F

Correction on mapping from virtual to physical resource blocks

15.6.0

2019-06

RAN#84

RP-191281

0014

2

F

Corrections to 38.211 including alignment of terminology across specifications

15.6.0

2019-06

RAN#84

RP-191281

0015

-

F

Clarification regarding non-full-duplex UE communication

15.6.0

2019-06

RAN#84

RP-191281

0016

-

F

Corrections on PUSCH scheduled by RAR UL grant and Msg3 PUSCH retransmission

15.6.0

2019-09

RAN#85

RP-191940

0017

-

F

Correction on PUSCH scrambling

15.7.0

2019-09

RAN#85

RP-191940

0018

-

F

Correction on PDSCH resource allocation scheduled by PDCCH in Type 0 common search space

15.7.0

2019-09

RAN#85

RP-191940

0019

-

F

Corrections to 38.211 including alignment of terminology across specifications in RAN1#98

15.7.0

2019-12

RAN#86

RP-192624

0022

-

F

Corrections to 38.211 including alignment of terminology across specifications in RAN1#98bis and RAN1#99

15.8.0

2019-12

RAN#86

RP-192634

0020

1

B

Introduction of remote interference management

16.0.0

2019-12

RAN#86

RP-192635

0023

-

B

Introduction of two-step RACH

16.0.0

2019-12

RAN#86

RP-192636

0024

-

B

Introduction of NR-based access to unlicensed spectrum

16.0.0

2019-12

RAN#86

RP-192637

0025

-

B

Introduction of integrated access and backhaul for NR

16.0.0

2019-12

RAN#86

RP-192638

0026

-

B

Introduction of V2X

16.0.0

2019-12

RAN#86

RP-192639

0027

-

B

Introduction of eURLLC support

16.0.0

2019-12

RAN#86

RP-192641

0028

-

B

Introduction of MIMO enhancements

16.0.0

2019-12

RAN#86

RP-192643

0029

-

B

Introduction of NR positioning support

16.0.0

2019-12

RAN#86

RP-192646

0030

-

B

Introduction of enhanced support for dynamic spectrum sharing

16.0.0

2019-12

RAN#86

RP-192646

0031

-

B

Introduction of additional RACH configurations for TDD FR1

16.0.0

2019-12

RAN#86

RP-192645

0032

-

B

Introduction of cross-carrier scheduling with different numerologies

16.0.0

2020-03

RAN#87-e

RP-200186

0033

-

F

Corrections to integrated access and backhaul for NR

16.1.0

2020-03

RAN#87-e

RP-200192

0034

-

F

Corrections to NR positioning support

16.1.0

2020-03

RAN#87-e

RP-200184

0035

-

F

Corrections to two-step RACH

16.1.0

2020-03

RAN#87-e

RP-200194

0036

-

F

Corrections to cross-carrier scheduling with different numerologies

16.1.0

2020-03

RAN#87-e

RP-200185

0037

-

F

Corrections to NR-based access to unlicensed spectrum

16.1.0

2020-03

RAN#87-e

RP-200187

0038

-

F

Corrections to V2X

16.1.0

2020-03

RAN#87-e

RP-200190

0039

-

F

Corrections to MIMO enhancements

16.1.0

2020-06

RAN#88-e

RP-200687

0040

1

F

Corrections to NR-based access to unlicensed spectrum

16.2.0

2020-06

RAN#88-e

RP-200694

0041

1

F

Corrections to NR positioning support

16.2.0

2020-06

RAN#88-e

RP-200692

0042

1

F

Corrections to MIMO enhancements

16.2.0

2020-06

RAN#88-e

RP-200686

0043

1

F

Corrections to two-step RACH

16.2.0

2020-06

RAN#88-e

RP-200696

0044

1

F

Corrections to carrier aggregation with unaligned frame boundaries

16.2.0

2020-06

RAN#88-e

RP-200689

0045

1

F

Corrections to V2X

16.2.0

2020-06

RAN#88-e

RP-200688

0046

1

F

Corrections to integrated access and backhaul for NR

16.2.0

2020-09

RAN#89-e

RP-201804

0047

-

F

CR on 2-step RACH for 38.211

16.3.0

2020-09

RAN#89-e

RP-201812

0048

-

F

CR on correction half duplex operation during DAPS HO

16.3.0

2020-09

RAN#89-e

RP-201807

0049

-

F

Corrections to V2X

16.3.0

2020-09

RAN#89-e

RP-201809

0050

-

F

Corrections to MIMO enhancements

16.3.0

2020-09

RAN#89-e

RP-201811

0051

-

F

Corrections to NR positioning support

16.3.0

2020-09

RAN#89-e

RP-201805

0052

-

F

Corrections to NR-based access to unlicensed spectrum

16.3.0

2020-12

RAN#90-e

RP-202380

0053

-

F

CR on the determination of DMRS sequences in 38.211

16.4.0

2020-12

RAN#90-e

RP-202383

0054

-

F

Correction on sidelink timing definition

16.4.0

2020-12

RAN#90-e

RP-202381

0055

-

F

Correction to UE assumption on RB set configuration for PRACH

16.4.0

2020-12

RAN#90-e

RP-202381

0057

-

F

CR to 38.211 on NR-U PRACH RO configuration

16.4.0

2020-12

RAN#90-e

RP-202383

0058

-

F

Corrections on sidelink for PHY layer structure

16.4.0

2020-12

RAN#90-e

RP-202383

0059

-

F

Correction on SL PT-RS sequence generation

16.4.0

2020-12

RAN#90-e

RP-202383

0060

-

F

Correction on PSFCH mapping

16.4.0

2020-12

RAN#90-e

RP-202387

0062

-

F

Corrections to 38.211 for NR positioning

16.4.0

2020-12

RAN#90-e

RP-202381

0063

-

F

CR to 38.211 to correct CP extension for SRS

16.4.0

2020-12

RAN#90-e

RP-202398

0064

-

F

Alignment CR for TS 38.211

16.4.0

2021-03

RAN#91-e

RP-210049

0065

-

F

Correction on DM-RS presence with PDSCH mapping type B

16.5.0

2021-03

RAN#91-e

RP-210049

0066

-

F

Correction on usage of subCarrierSpacingCommon for unlicensed

16.5.0

2021-03

RAN#91-e

RP-210050

0067

-

F

Clarification on Sidelink SSID

16.5.0

2021-03

RAN#91-e

RP-210059

0068

-

F

Alignment of notation

16.5.0

2021-06

RAN#92-e

RP-211248

0069

-

F

Correction on RIM RS resource and set ID mapping

16.6.0

2021-06

RAN#92-e

RP-211236

0070

-

F

Correction on channel inference assumption for PUSCH repetition Type B

16.6.0

2021-06

RAN#92-e

RP-211243

0071

1

F

Alignment of notation

16.6.0

2021-06

RAN#92-e

RP-211235

0072

-

F

Correction on OFDM signal generation and PSSCH DM-RS time-domain OCC in TS 38.211

16.6.0

2021-06

RAN#92-e

RP-211233

0074

-

A

Correction on channel properties assumption of UL transmission

16.6.0

2021-09

RAN#93-e

RP-211850

0076

-

F

Alignment of notation

16.7.0

2021-12

RAN#94-e

RP-212958

0078

-

A

Correction to CCE-to-REG mapping and CSI-RS mapping

16.8.0

2021-12

RAN#94-e

RP-212960

0079

-

F

Correction to VRB-to-PRB mapping for DCI format 1_2

16.8.0

2021-12

RAN#94-e

RP-212966

0080

-

B

Introduction of MIMO enhancements

17.0.0

2021-12

RAN#94-e

RP-212967

0081

-

B

Introduction of extensions to 71 GHz

17.0.0

2021-12

RAN#94-e

RP-212969

0082

-

B

Introduction of Non-Terrestrial Networks (NTN)

17.0.0

2021-12

RAN#94-e

RP-212973

0083

-

B

Introduction of coverage enhancements

17.0.0

2021-12

RAN#94-e

RP-212979

0084

-

B

Introduction of Multicast and Broadcast Services (MBS) support

17.0.0

2021-12

RAN#94-e

RP-212982

0085

-

B

Introduction of DL 1024QAM for NR FR1

17.0.0

2022-03

RAN#95-e

RP-220920

0086

2

C

Pi/2-BPSK specification updates for the merger of 5Gi into 3GPP

17.1.0

2022-03

RAN#95-e

RP-220245

0088

-

A

CR on corrections on SL timing

17.1.0

2022-03

RAN#95-e

RP-220251

0089

-

F

Corrections to NR in the 52.6 – 71 GHz range

17.1.0

2022-03

RAN#95-e

RP-220263

0090

-

F

Corrections to NR support of multicast and broadcast services

17.1.0

2022-03

RAN#95-e

RP-220250

0091

-

F

Corrections to MIMO enhancements

17.1.0

2022-03

RAN#95-e

RP-220252

0092

-

F

Corrections to IIoT and URLLC enhancements

17.1.0

2022-03

RAN#95-e

RP-220253

0093

-

F

Corrections to NR NTN support

17.1.0

2022-03

RAN#95-e

RP-220270

0094

-

F

Corrections to small data transmissions in RRC_INACTIVE state

17.1.0

2022-06

RAN#96

RP-221606

0095

-

F

Corrections on NR UE Power Saving Enhancements

17.2.0

2022-06

RAN#96

RP-221600

0096

-

F

Corrections to MIMO enhancements

17.2.0

2022-06

RAN#96

RP-221603

0097

-

F

Corrections to timing advance for NTN

17.2.0

2022-06

RAN#96

RP-221620

0099

-

A

Clarification of PUSCH DM-RS generation

17.2.0

2022-09

RAN#97-e

RP-222401

0100

-

F

Correction on the subcarrier offset, kssb

17.3.0

2022-09

RAN#97-e

RP-222406

0101

-

F

Corrections on UE Power Saving Enhancements for NR in TS 38.211

17.3.0

2022-09

RAN#97-e

RP-222412

0102

-

F

Corrections to NR support of multicast and broadcast services

17.3.0

2022-12

RAN#98-e

RP-222863

0103

-

F

Correction on sidelink timing

17.4.0

2022-12

RAN#98-e

RP-222864

0104

-

F

Corrections to NR support of multicast and broadcast services

17.4.0

2023-06

RAN#100

RP-231226

0105

1

F

Alignment of parameter names

17.5.0

2023-09

RAN#101

RP-232449

0107

-

F

Alignment of terminology across specifications

17.6.0

2023-09

RAN#101

RP-232469

0108

-

B

Introduction of NR sidelink evolution

18.0.0

2023-09

RAN#101

RP-232480

0109

-

B

Introduction of expanded and improved NR positioning

18.0.0

2023-09

RAN#101

RP-232458

0110

-

B

Introduction of MIMO evolution for downlink and uplink

18.0.0

2023-09

RAN#101

RP-232477

0111

-

B

Introduction of NR support for dedicated spectrum less than 5MHz for FR1

18.0.0

2023-09

RAN#101

RP-232470

0112

-

B

Introduction of dynamic spectrum sharing enhancements

18.0.0

2023-09

RAN#101

RP-232471

0113

-

B

Introduction of multi-carrier enhancements

18.0.0

2023-12

RAN#102

RP-233722

0114

-

B

Introduction of additional PRS configurations [1symbol_PRS]

18.1.0

2023-12

RAN#102

RP-233707

0115

-

F

Corrections to NR Dynamic Spectrum Sharing (DSS)

18.1.0

2023-12

RAN#102

RP-233716

0116

-

F

Corrections to NR support for dedicated spectrum less than 5MHz for FR1

18.1.0

2023-12

RAN#102

RP-233705

0117

-

F

Corrections to MIMO enhancements

18.1.0

2023-12

RAN#102

RP-233718

0118

-

F

Corrections to NR Network-controlled Repeaters

18.1.0

2023-12

RAN#102

RP-233719

0119

-

F

Corrections to positioning enhancements

18.1.0

2023-12

RAN#102

RP-233733

0120

-

B

Introduction of multicast reception in RRC_INACTIVE

18.1.0

2024-03

RAN#103

RP-240518

0122

-

F

Corrections to MIMO enhancements

18.2.0

2024-03

RAN#103

RP-240528

0123

-

F

Corrections to positioning enhancements

18.2.0

2024-03

RAN#103

RP-240535

0125

-

A

Alignment of parameter names

18.2.0

2024-03

RAN#103

RP-240519

0126

-

F

Corrections to sidelink enhancements

18.2.0

2024-06

RAN#104

RP-241061

0127

-

F

Correction for hop counting in SRS for positioning with tx hopping

18.3.0

2024-06

RAN#104

RP-241075

0128

-

F

CR for 38.211 on TRS occasions for idle/inactive UEs

18.3.0

2024-06

RAN#104

RP-241076

0129

-

B

CR for TS 38.211 for introduction of FR2-NTN

18.3.0

2024-06

RAN#104

RP-241061

0130

-

F

Corrections to positioning enhancements

18.3.0

2024-06

RAN#104

RP-241072

0131

-

F

Corrections to sidelink enhancements

18.3.0

2024-06

RAN#104

RP-241059

0133

-

A

Corrections to NTN operation

18.3.0

2024-09

RAN#105

RP-242209

0134

-

F

CR on Precoding Matrices for 8TX UL MIMO Transmission

18.4.0

2024-09

RAN#105

RP-242205

0135

-

F

Correction on bandwidth part for SRS frequency hopping for positioning

18.4.0

2024-09

RAN#105

RP-242205

0136

-

F

Correction on staircase pattern for SRS frequency hopping for positioning

18.4.0

2024-09

RAN#105

RP-242210

0137

-

F

Correction on determination of restricted type for candidate cell PRACH transmission in LTM

18.4.0

2024-09

RAN#105

RP-242204

0138

-

F

Alignment of parameter names

18.4.0

2024-09

RAN#105

RP-242203

0140

-

A

Alignment of parameter names

18.4.0

2024-12

RAN#106

RP-242931

0141

-

F

Correction on mapping PSFCH to physical resources

18.5.0

2024-12

RAN#106

RP-242930

0143

1

F

Correction on the open loop timing advance calculation for ATG

18.5.0

2024-12

RAN#106

RP-242924

0145

1

A

Alignment of parameter names

18.5.0

2024-12

RAN#106

RP-242925

0146

1

F

Alignment of parameter names

18.5.0

2024-12

RAN#106

RP-242929

0147

-

F

Corrections to PRACH transmission for LTM

18.5.0

2025-03

RAN#107

RP-250225

0148

-

F

CR on PSCCH DMRS sequence generation in a dedicated SL PRS resource pool

18.6.0

2025-03

RAN#107

RP-250226

0149

-

F

Alignment of parameter names

18.6.0

2025-06

RAN#108

RP-251564

0150

-

F

CR on SRS hopping for positioning in TS 38.211

18.7.0

2025-06

RAN#108

RP-251836

0151

-

B

Introduction of sub-band full duplex (SBFD)

19.0.0

2025-06

RAN#108

RP-251577

0152

-

B

Introduction of low-power wake-up signal

19.0.0

2025-06

RAN#108

RP-251580

0153

-

B

Introduction of NR MIMO Phase5

19.0.0

2025-06

RAN#108

RP-251583

0154

-

B

Introduction of NR_NTN_Ph3

19.0.0